What power tools should I add

Not power but speed square and a long spirit level that's 2-3 ft.
Small 2-2.5 gal. wet/dry Shop Vac is what I use to pull remaining water from toilet tank when changing fill valve and cleaning up dust after small jobs in rooms.

All mentioned above are definitely worth having when necessary:

Oscillating tool
Impact driver
Shop vac - I would get one with a stainless steel body. Easier to clean and lightweight compared to plastic.

Things you can add that weren't mentioned:
Angle grinder
One-handed hackzall (the small version of a sawzall)
Jigsaw

I use the hell out of my miter saw, drill, impact driver, socket sets, oscillating tool, angle grinder

Some good advice if you're looking for a small sized tool bag. I have 3 shop buildings full of tools, so it's hard to pare it down to basics.

But ill add a dead blow hammer. I use that thing on everything from putting together woodworking joints, to metalworking and all sorts of stuff.

Sometimes things need some persuasion and a dead blow hammer is an inexpensive tool that fits the bill.

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Oscillating tool

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One of the MUST-HAVE power tools every DIYer needs.

I will give the same advice I always give on woodworking forums buy what you need for each upcoming project. This is especially true if you are on a budget. The chances you will correctly anticipate the exact tool you need next are low. Years ago when budget was more of a constraint I would buy one or two tools for each new project that made it faster, easier, or produced better results. I always made sure to still be saving significant money over hiring it done. Over time you will build up quite a few tools AND they will be geared to the projects you actually do. For example, I use a clamp on multi-meter quite often, in fact, I have been ask by friends twice in the last few weeks to borrow mine. It happens enough I bought a cheap one to loan, I am not loaning even a friend my Fluke 87 w/ an i400 clamp to bugger up.

This was the advice I was going to offer, by them as you need them.

RotoZip with flush cut attachments. Jigsaw. Stud Finder. Plumb Bob.

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Angle Grinder. Good to sharpen garden tools, cut off rusted bolts, and lots of other random things.

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Just a word of caution on angle grinders and specifically with cutoff wheels. I'm pretty lax with safety when using tools, but I've had more close calls with the angle grinders than I have any other high speed spinning tools that I've used. I do weld very frequently and use angle grinders more than any other tool granted, but if you're cutting something and it grabs, you'll be missing a finger and/or in the ER faster than you can realize. It took me a couple of close calls to figure out how to avoid material pinching the blade.

TLDR: Be very careful with angle grinders.