But using your reaction to counterspell shield (the example) between two attacks you are talking with your action is NOT explicitly in the rules and nothing I've seen would suggest this example is any different than using another type of action (bonus action, action surge action, haste action, or object interaction) between your two attacks.
Well, the rules for Bonus Actions states that: "You choose when to take a bonus action during your turn, unless the bonus action's timing is specified". That's about as tacit permission to use one whenever as you can get. (PHB 189)
And Reactions state that "a reaction is an instant response to a trigger of some kind, which can occur on your turn on on someone else's". (PHB 190) If you can't use a reaction when the trigger comes up, it would be a pretty useless ability.
Curiously I've noticed a discrepancy. Page 189 states that: "You decide whether to move first or take your action first", but then page 190 gives us "Breaking Up Your Move", which tells us that you can use some of your speed before or after your action, and even move between weapon attacks.
It's not wrong that you can move or act first, but it kind of muddles the actual rule which is that you can split up your move mostly however you like on your turn, with the exception of non-weapon attacks (probably).
Though unstated, I assume you can drop Prone or stand up at any time you could move.
At any rate, what we're left with is, it never states you must complete an action before you can take another kind of action. It can be inferred from the text that since some things tell you that you can do them whenever, that the default is that you can't, but this leads to odd situations in either respect.
For example, my prior example of Use an Object. You can do this once per turn without taking an action. Thus a character could take the Attack Action, make an attack, then if they have the need, interact with another weapon to make a second attack, and I don't think there's any issue with this.
If you're a Thief and you want to use your bonus Action to Use an Object, since no timing is specified, no problem. But somehow using Action Surge or Haste, which are additional actions on your turn, you couldn't? Seems odd to me.
But on the other hand, stopping between attacks during an attack action to launch a spell or use a magic item could be seen as problematic, though there's not many ways to do this.
It occurs to me, however, that you totally can do all these things, if you know what you'll need to do at the start of your turn- for example, I could Ready an action and set a trigger that happens "after I attack", Action Surge, take the Attack Action, attack, have my Readied reaction go off, then continue.
And if this is the case, it seems to be the ultimate in splitting hairs to be like "haha, you had no idea you'd run into a complication during your turn that would require you to set up a Readied Action, so you can't do that now".