2500 is bottom of zero turn price, so I would be careful on buying one in that price range. I am sure there are some good deals, but I would be careful.
2500 is a good price range for the tiny riding mowers. You don't need the bigger deck or larger engine, buy a better engine brand and a better built mower and stay in the smaller size. And even then, 2500 can easily be blown on these from what I recall.
The thing about a riding mower is you have a conventional setup and probably easier repairs.
I have a couple zero turns in the extended family and getting into hydraulic drive vs. belt annoys me. Sure hydraulics are well proven and better for many reasons than belt drive. But you know what I like about belts? I can buy a belt at about any napa or on the net and replace it myself and not be out anywhere near the price for some of this hydraulic stuff.
Now if the hydraulic stuff can be rebuilt with new seals on my workbench, that is something to consider. One uncle said they could not be readily rebuilt so he replaced em. Not cheap.
I also like being able to hook a tiny trailer up to my riding mower for little stuff. I have a little trailer to start with but I also like being able to hook stuff up and drag it with the mower or use it to pull the mower loose.
Zero turns handle some slopes, do some reading on em and decide for yourself.
I would not like using them on slopes but I know from what gets mowed by my uncles that they work well on slopes I would not touch. I have borrowed one of their zero turns in the past and yes it is faster. Yes it has a learning curve. Yes I would like to own one but for just mowing I can not justify it due to the slope limitations.
I do have an atv for the little trailer if I got a zero turn. But the riding mower setup works well for me, I can easily work on it and know the basics to most riding mowers already. And yeah my riding mower has the old belt drive stick shift transmission, I don't get along with hydrostatic very well. Back to that hydraulic thing I guess.
Most of my stuff is bought used, repaired as needed. Replaced when a better handme down or used item is found or I outright blow something up but that is rare.
I had slopes to mow and a lot of mowing to do a decade ago. I was sort of in your price range, wound up at 3k with tax and all.
Bought a brand new 36 inch exmark metro belt drive walk behind mower. This is a well built unit that has lasted better than I expected. I don't know what they cost now but mine is still running fine and did need new tires due to dryrot. Had a tune up, gas tank cleaning, carb cleaning, and eventually it will even get some plugs. It gets an oil change and filter each year or so, depends on how much I use it.
Due to slopes I was mowing no riding mower or zero turn would work, this one earned its keep well and while not an option you listed it might be something to consider used perhaps.