Own a few homes, while there's a huge list of "must have" tools, most are also pretty common. Here's my odd tools I can't do without:

Cat's Paw Prybar is amazing for pulling nails that are smaller, sit more flush, or are in harder to reach locations.

Gas Can Conversion Kit because the new gas cans spill all over and are a pain in the ass to use. I won't subject myself to that, and it's easy to convert most gas cans over to the standard spout/vent style.

For those with old homes with plaster/lathe walls, you can find studs by putting a hard drive magnet or other very strong magnet on a string. It'll find the nails where the lathe is nailed to the studs.

Wago 221 Lever Nuts while I do still like wire nuts for solid wire home wiring (be sure to pre-twist!), when doing light fixtures, dimmers, or other cases where you'd be connecting solid to stranded wire or stranded to stranded wire, these things are a HUGE game changer.

A small bin like this every dang time I find a leak from a kitchen faucet or go to work on the toilet and have to disconnect the water supply, my normal 5gal pails or other containers are either too tall, too small to hold the water, or have other issues. A bin that's shallow yet large like this can handle all your drips and spills when working on plumbing. You probably already have something like this, but designating one as a workhorse for toilet water or sink trap water is great.

If you have a dog, get a Lily Brush, this thing is MAGIC for getting hair off fabric, I use it all the time on my couch and in my car, helps make vacuuming up dog hair so much easier.

Every homeowner should own a pair of quality knee pads, but so many people don't. Find a pair that fits your needs well, don't cheap out and save your knees. Good for working low in the house, gardening, pulling weeds in the driveway, etc.

Pipe Dope toss that teflon tape in the garbage, get some pipe dope. Way easier to use, gives a more consistent seal, makes you worry less about water/gas connections. Costs a bit more than tape, worth it.

Re-usable hearing protection. I've got these, they're great for when I mow the grass, snowblow, leaf blow, or weed whack. There's cheaper options out there that are fine to have/use, but I like listening to music and such while I work. Love them, and my wife appreciates me taking care of my hearing!

Smart Garage Door Opener ever have a mini panic attack because you can't remember if you closed your garage door or not? Want your garage door to automagically shut every night so you never forget at night? Ever want to remotely let someone into your house when they come to grab a shovel? These things are shockingly cheap and are a game changer to have.