If you use your phone a lot imo it's worth getting a new one so you don't have to constantly worry about your next charge

Buy a new battery.

What about a battery replacement?

Depends on what do you use your phone for. If you often use it then just buy another one or change the battery.

I'd leave it untill it's only 1 hours of screen time then get a new one. So I'd charge it on the work computer first then get the power bank after then get the new phone once it's stopped working.

Charging it on the work computer would be cheaper and greener than buying a power bank, but computers charge very slowly; it might not even charge as fast as your phone consumes energy. Also, you obviously won't be able to use your phone for more than 3 hours outside of work or somewhere else with a charging port without a power bank, so it depends on whether you'd want to do that. I wouldn't get a whole new phone; you already have a better one, and buying a power bank will be cheaper than even a cheap phone and will allow you to use it for as long as you want.

You could just leave it on the charger for a time, but I'd get the best new device I could afford unless my old model had a battery that's not a nightmare to swap out - unfortunately most devices these days are intentionally designed to have irreplaceable parts to make you buy new SMH