MacBook Pro 2015 13-inch, left shift key stuck after battery replacem

I don’t see your issue is related to the logic board, it would be very difficult for you to damage it with the solvent. You could have damaged a component in the process of prying the battery out. But even that wouldn’t effect only one key on your keyboard.

Now looking at solvent dripping down into the keyboard which is just on the other side of the logic board. That is also not likely unless you flooded things letting the solvent to drip through the few gaps in the uppercase. Even still you would have encountered an issue right away as the solvent would have evaporated leaving the keyboard in a bad state within an hour at most.

So where does that leave us??

Sadly, I think you just encountered a failed key issue independently of your battery replacement. Let’s dig a bit deeper into what’s happening with the given key. Using an external keyboard open your Systems Preferences > Keyboard. Now check on ‘Show keyboard and emoji viewers in menu bar’

Now clicking on the menu bar icon and sliding down to Show Keyboard Viewer You’ll have access to it

As you can see here I’ve enabled the Caps Lock, check your Shift key does it work at all?

Sadly, it’s time to replace the keyboard

This is not an easy job! You’ll need to strip the system down to get to the uppercase following this guide 交换MacBook Pro13'' Retina显示器 2015早期版本的上部机身

Once you are this point you have two directions swapping out the uppercase with a new keyboard (the easier direction) MacBook Pro 13" Top Case & US Keyboard, Apple P/N 661-02361 or carefully lifting the backlight assembly (black sheet) to gain access to the screws and rivets which hold the keyboard MacBook Pro 13" Retina (Late 2013-Early 2015) Keyboard this is quite hard!