Depends how you use the space, but you could convert it to a pea gravel patio. https://www.liveinyourbackyard.com/patio-deck/the-pros-and-cons-of-a-pea-gravel-patio/

It looks to me more like a 'sport court' than a patio. Just a paved area where kids could ride tricycles, bounce balls, and generally run around when the lawn is too wet or snowy. If you don't use it, I'd get rid of it. If you find out in a few years that you want a large patio, then you can put one back in.

You will not be able to remove the concrete yourself. Unless you own a skidsteer with a hydraulic jackhammer and 6-wheel dump truck to haul the massively heavy and large cubic foot of concrete away to the crusher.

It is possible to overlay concrete with pavers or mortar a tile/brick if you are in a non-freezing climate. However, it has to be done over an existing concrete slab that was installed properly and has no deterioration or ongoing problems, and it appears your slab is not a candidate for that. You could extend a larger wood platform from the existing stoop that floats on top the slab, as most jurisdictions would not require an official deck and footings for something only 1 step up, but I would consider that to not be a long-term solution because of the slab condition and how it looks to collect water from the surrounding grade.

Best suggestion is just to wait until your coffers replenish, and come up with a plan during that time for an outdoor living space that meets your lifestyle and use and works with the house layout.

Deck tiles (over dirt) might be an option:

https://aprylann.com/interlocking-patio-tiles-over-grass/

Search ’deck tiles’ for more information and prices. We’re thinking of using them off our patio to extend the seating area.

I’m still gathering info about it myself, so can’t say if it would work for you.

Another idea, and one we’ve done, is looking around for someone selling/free pavers, stones, etc. Some people are glad to have someone haul away what they don’t want.

"You will not be able to remove the concrete yourself."

Sure you can!! Been there, done that (actually 60 feet of driveway). Helps if more than one set of hands involved. A cracked concrete slab is actually relatively easy to break up manually with a prybar and sledge. Or you can rent a jackhammer if thicker than around 6 inches.

We recycled all the concrete chunks at 2 other of my landscaping projects. 3/4 ton pickup and multiple loads, but completely doable. Recycled concrete is typically an in-demand landscape material in my area and posting a "free - you haul" offer on Facebook or Nextdoor, etc. will remove any disposal issues :-)

btw, pea gravel makes a very poor patio base. Uncomfortable/not easy to walk on and difficult to site table and chairs or lawn furniture. And it migrates.

25'x35' = 11 cu yards and over 20,000lbs ! And hopefully no wire mesh sitting on bottom!

It does't appear to be that bad. I'd investigate an overlay.