I don't follow your logic. The rules here explicitly state that the move portion can only be towards the target and the MBA (or bull rush) can only be against the same target.
What you are claiming is that the standard actions that include attacks are not themselves attacks which doesn't really make sense:
I'm not 'claiming' anything, ITS TRUE, read the rules. By RAW 'actions which include some sort of recipient of the action' aren't attacks, and the rules on targets explicitly talk about them only in terms of attack powers. In fact its even a bit unclear as to targets of utility type powers since no attack exists, and you do run into some issues there as well. Strictly speaking an ACTION isn't an attack. You use the "Use a Power" action, select an attack power, and the power is the attack in all cases, not the action.
The cases of things like Bull Rush where you have an action that targets an opponent and logically should be an attack are just an example of poor rules structuring. When WotC wrote the online compendium notice that they took virtually all of these cases and constructed a power block to represent the action. They should have done this from the start and it would be more consistent, but I assume they didn't want to burn page space. You are certainly encouraged (by me at least) to apply the rules for attack powers to these cases, but BY RAW this is not how it works. We assume RAI is that a Bull Rush is an attack and effectively a power, its just not so by RAW. Charge is an even more complex case.
Aid Another. Not an attack because although the standard action includes the attack roll of an attack power, the action itself is not an attack power (like Basic Attack).
Clearly not an attack, that's right. This works fine.
Bull Rush. Not an attack because although the standard action includes an attack roll, the action itself is not an attack power.
Technically correct, by RAW a Bull Rush isn't an attack because no power is used, and only attack powers can be attacks. This is the most clear case of an action that SHOULD be a power and I'd assume virtually all DMs would treat it as such.
Charge. Not an attack because although the standard action can include an attack power, the action itself is not an attack power.
Nope, not an attack. This case is a little different from Bull Rush since there IS an attack power being invoked in the attack phase of the charge. Still, the movement phase is not an attack and the target of the charge isn't the target of an attack and doesn't invoke those rules until the attack portion. Instead it follows the charging rules themselves. There are cases where its useful to extent the conventions of attacks to the target of a charge, but by RAW its a separate thing.
Coup De Grace. Not an attack because although the standard action includes an attack power, the action itself is not an attack power.
Well, this is trivial. Its just as much an 'Attack' as any other "Use an Action" would be, the power makes an attack, so there's nothing weird going on here.
Grab. Not an attack because although the standard action includes an attack roll, the action itself is not an attack power.
True, and this has caused no end of debates and rules conundrums just like Bull Rush has. Again, its usually best to consider the Grab as being a power block, and I believe WotC has written it up so online, but RAW is a little ambiguous.
Opportunity Attack. Not an attack because although the standard action includes an attack power, the action itself is not an attack power.
Obviously. Again, this is the same as any other use of an attack power, the underlying action isn't itself an attack.
Ready. Not an attack because although the standard action can include an attack power, the action itself is not an attack power.
Ready An Action isn't really DOING anything, its just declaring an intent. The triggered action when it happens is generally used to make an attack, which is again just an attack and the same distinction exists as ever, the action is an action and the attack power you use is an attack.
Sorry, none of these make sense from an interpretation POV. All of these standard actions are attacks. If they include an attack roll to hit or they use an attack power, they are an attack. Aid Another is just as much an attack as Basic Attack is. The results are just different.
Example: Cleric uses Astral Seal. Rogue uses Aid Another. If the Rogue hits with his Aid Another attack, he gets the hit points from the Astral Seal.
Nope, not by RAW, this is simply incorrect. AA is not an attack, its never described as such in the rules and using it (or Bull Rush or Grab) WILL NOT invoke the effects of Astral Seal or any other similar power, nor qualify the Rogue to do something or attain some benefit of an attack. Bull Rush and Grab probably SHOULD be attacks, and I think most of us will go with RAI (and some online representations of the rules) on this, but I see no justification for AA ever being an attack personally, though I guess its possible that it could be narrated as such in some cases.
All of these standard actions are just special rules about the attack that limit or enhance the attack. It's still an attack.
You can say that till your blue in the face, it doesn't make it RAW.
And if an action includes movement, a Readied action can interrupt it.
Movement is a different issue. It is defined by a whole different set of rules than attacks and a discussion of one is not germane to the other. Even so I would point out that there are some analogous issues WRT movement, like "can falling trigger an OA?"
Finally, there are two only standard actions that fall into your category of an attack must be an attack power: Basic Attack and Use a Power. But there is nothing special about either of these in the rules that preclude other standard actions from being attacks.
It isn't a matter of preclusion. First of all 'Basic Attack' isn't an action, it is a power, invoked via the 'Use A Power' action. Again, it isn't a matter of the rules 'precluding' anything, it is a matter of what they INCLUDE, which is rules for making attacks using Attack Powers. Read the combat chapter, it is clearly and entirely formulated around describing attacks in terms of powers, and says nothing about any sort of "non-power attack". Targets are chosen in accordance with the target blocks of powers, their ranges, and attack types, attack rolls are described in terms of 'attack' blocks, etc. It is quite true that other parts of the rules are written more loosely, but they don't really explicitly state rules for how to make non-power attacks. Its just something the reader is left to determine for themselves. Its not HARD in a basic sense, but as your example of Astral Seal illustrates 4e is a complex game and it can become a little messy when you have other interacting rules.
Also, I don't think that you have a rules quote for your claim that "only powers can be attacks". A grab is an attack. It's just not an attack that requires an attack power. I could claim "That is exceedingly plain from any reasonable reading of the rules".
I think the INTENT is pretty plain. The actual formal structuring of the rules which is normally meant by people when they, for example, answer questions on the WotC Q&A thread about RAW is not so plain. Does a Bull Rush trigger an Astral Seal benefit? By absolute letter of the law of the rules, no it doesn't. SHOULD it? PROBABLY, but lets be clear here, all rules are worthy of interpretation. I've seen cases of uses of attack powers where the narrative wouldn't clearly justify triggering an Astral Seal benefit, so its not like ANY part of the rules doesn't get interpreted. Its only a matter of what your preferences are. This is why I always try to answer questions in terms of RAW, because its not up to me to decide what interpretation is appropriate beyond that unless we're talking about a very specific situation. When people ask "what are the rules", then they should get the answer that the rules give.