UngeheuerLich
Legend
Why do you want to build a combat alchemist (you can add quite some damage, but it really is not its strength).Armorer looks a lot of fun level 9. I think they need half of that ability earlier and the rest at 9.
All artificers get decent lvl 10 I can even build an ok combat alchemist that level.
I really think, you have too many long rests. A (basic) rogue at level 7 is only strong if you have more than one encounter per rest, since the rogue is neither reliant on short nor long rests.
In the most simple way they attack with advantage for 5d6+4 damage at level 7 and can reduce incoming damage quite well.
An alchemist has a 2d10+4 damage cantrip and can have a flaming sphere up in 3 combats with a good concentration saving throw. They can also hand out some useful potions and flash of geniuses and magic items.
It does not compare to what a bard is doing at that point, but that is difficult anyway.
An artillerist at that point does 2d10+1d8 damage and 2d6 area damage as an off hand attack without spending meaningful ressources, which compares to the rogues contribution.
Both are decent with thieves tools.