Heck I'd probably fund a couple tenure positions at a university on the condition that they research certain problems and publish everything to an open access journal. What does a bio lab cost to run, would 10 million a year cover it? That'd be 100 years of funding for 10% of my wealth.
I'd probably follow it up by going to one of my cities troubled youth schools and offering full ride scholarships to everyone who graduates. Figure 100 students a year, 100k scholarship, that's another 10 million a year, so another 10% gone.
Tl;Dr I'm having no problems figuring out how to spend 10 billion!
Somethings that could interest you:
A private island?
A megayacht?
A mansion/penthouse in a ritzy part of LA/NYC (Bezos's LA mansion alone was 1XX MM)?
A professional sports team?
A private jet?
The ability to call the leader of your country and either get through or get a meeting on the books?
Notice that what's interesting about a lot of those isn't just the initial cost, but many of them have quite high carrying costs.
But those are just interesting generalities. At that wealth you can (really have to) get creative. Paul Allen bought a bunch of rock star's guitars and a bunch of Sci Fi memorabilia, and then built a museum to hold them.
Where is that? Are you planning on living in the country? In most large cities, it doesn't seem like 10MM will be enough for you to live in an estate and still not have to work for ongoing regular expenses (food, etc.)
And it's fine you don't want any of those things. Better than fine, that's great. But there are a lot of things that you need more than 10MM for.
A private jet.
You could start a company that builds rockets to go explore Mars.
In other words, you could do something great.
Influence on the global stage
The ability to finance meaningful changes to the world - be they things like disease eradication, political movements, space endeavors. Rather than needing to band together with like-minded individuals and bring a voice to the table, you can outright create or buy a group to enable your vision (within the constraints of physics, and the political overton window)
At 10M, you have, as you say, a modest discretionary budget. Which is to say, it's modest, and not extravagant. The things you can do frivolously while spending $300k/year is different than what you can do while spending $1mm/year, but as you've discovered, unless you get disgustingly ostentatious (I hear the poors only own one car, and drive the same car for longer than a month.), taking care of your creature comforts in a reasonable way isn't that expensive. Eating $400 steak dinner every night for a year is only $150k/yr ("only"). So, other than get ostentatious (what, you don't have multiple houses in multiple states?), what do you do? Change the world.
I mean, congratulations on having joined the two comma club, your little discretionary budget is cute. At 10B, your discretionary budget is probably not actually 1000 times larger, because that's a different game of liquidity, but what you can do without remotely threatening your principal investments is way larger. At 10M, if there was a reason you had to spend $5mm, you'd have to consider it very strongly before doing it. At 10B, you can get $1mm in cash from the bank and light it on fire for the hell of it because you had nothing better to do on a Tuesday night. If there's a movie you want made, you get to ask whomever you want to star in it. You want to have a movie made about your life, starring Nick Cage as you? He's having money problems, so he'll probably say yes.
10B puts you right above Steven Rales, wikipedia article here: https://en.wikipedia.org/wiki/Steven_M._Rales. Which is to say, if you want to be a recluse, be a recluse, but 10b puts you in the club of people who have wikipedia articles written about them, despite not being a household name or noteable. Edward Snowden has a wikipedia article, and he's not a billionaire, but he was forced to do some world changey shit to get that. You'd get that simply for having that kind of money. Poke around the Forbes billionaire list - https://www.forbes.com/real-time-billionaires/. See how many names you recognize as household names. 10b automatically dumps you in those leagues. Marc Benioff's #240 with an estimated $10b. Now, you may not want to be, but if you're familiar with his work, you can do anything like that, on that level. Own a local sports team. It's a bit different rooting for the local sports team when it's your sports team.
Personally, I'd fund science and research and the arts rather than have anything to do with sports. Affordable healthcare. Buy buildings and give buildings to Planned Parenthood so they don't have to keep moving around (something about protestors makes their neighbors nervous). Fix homelessness (which is a big problem, but I'm sure $10m/yr would help lots of aspects of it). Start a chain of coffee shops and over-employ people so that the people that work there have regular weekly schedules and can go to college.
I hate to say it, but that's really a lack of imagination. Instead of $10M principle with a modest discretionary budget, think of the unreasonable shit you could do with $10m every year. Some of it could even be good for other people.
Mathematically, yes. Practically, so what? 10M is a number that could provide all I could reasonably want for the rest of my life. 10B puts a target on my back, and for what? What does 10B buy me that 10M wouldn't? A life of isolation and extravagance? I can't say that I would turn down the chance to find out, but I'm FI already, and maybe it's lack of imagination but I already have trouble spending my modest discretionary budget as it is.