It ties in to model engineering in some ways, but model making is a variation. I've started building wooden boat models and have always had an interest in model trains. The scenery component is more artistic and less technical. Evan a small diorama can make a nice way to display a model. You don't have to build the model or figures unless you want to, the diorama is in effect the stage set to display something. Great stage designers don't have to be actors.
If plastic model making done right looks interesting, see if there is an IPMS show coming up anywhere near you. IPMS is the "International Plastic Modelers Society". Yeah, I couldn't believe it the first time either

Incredible modeling and painting skills on display, the bigger shows have seminars as well. It's a long way from drug store car kits with that nasty gooey tube cement mess of our childhood.
Gardening is either very frustrating or a pleasant pastime, goes both ways for me depending on deer and rabbits :-( The hydroponic lettuce in the greenhouse is doing well, that and spinach are all we can grow this time of year as the cost to heat a greenhouse far outweighs the benefit we would receive. Here in Tidewater Virginia Mother****** Nature always wins. Since focusing on native plants my success rate at planting has gone way up and we aren't locked in combat trying to force a square plant into a round world.
Spending a morning a week doing the little jobs that get put on the "around to it" list is sort of satisfying and lets you get things done when it's cold and drizzly outside.
Not being morbid here, but having dealt with the clearing out of family members houses after they died, we've been pretty aggressively getting rid of accumulated stuff that fails the "Does this make me happy or make my life better?" test. All our kids have had the chance to call dibs on things we still want or were going to donate / sell. Boxes of old no longer interesting or relevant books go to the friends of the library for book sales, good but outgrown clothes and housewares to the DAV, next thing you know your house is cleaner, neater, and you only have stuff around you that you WANT. It's actually very satisfying to recover half a book case or a few drawers or a kitchen cabinet that was just a pile of stuff you dreaded opening. Now that I'm in the habit, every time I walk past a bookshelf or open a cabinet my thought is "Is there anything here I don't want, like, or need?" I had loads of old parts and partial projects for electronic gadgets that I never had time for while working. Now they would be obsolete, or can be done better with a $3 Arduino and a few cheap sensors and the finished gadget fits in an Altoids tin instead of in needing a 4U rack case. No reason to stick my kids with disposing of stuff overcome by events already. I admit to keeping some stuff purely out of sentiment, but those things pass the "does it make me happy" test.
My old business resulted in multiple copies of tools. Shop set, machine shop set, house call set, electrical and electronics shop set. Now I'm retired. It's wonderful to have good tools, but four or more of the same is just in the way when you condense the four + locations down to one or two. The kids got first dibs, then I gave the spares away at the local boat modelers or model rail club meetings. I've benefited greatly from others doing the same and from people freely sharing and encouraging others. No bad feelings about giving some stuff away and I get room in some top boxes and roll arounds. A win for all. When visiting one of the kids sometimes something needs repair. If than means buying a tool it stays with them most of the time. I surely don't need a fifth circular saw or four inch drywall blade.
Learning a musical instrument is alleged to be not only fun (??? - not always...) but also seems to help keep your brain a bit healthier. In the early 1970's our school had a Mini Moog synthesizer, but the teacher knew nothing about it and didn't want anyone to touch it. Always wanted to play. These days there are FREE synthesizers all over the internet you can play with if that's of interest. I'm not far past the beep boop screech phase of play, but it's fun. My arthritis in the fingers and wrists sadly has limited my guitar playing, but instead of giving up I'm learning to play slide.
The capability of digital image processing combined with the high quality images you can get even with just a smart phone is incredible. I came darn close to majoring in photography at RIT before going the down the shining path of nerddom. I can do in seconds what would have taken hours or been impossible back in the wet process days of photography. I'll put in a plug for ON1 Photo Raw if you have a Windows 10 or higher machine with a GOOD mid to high range NVidia graphics card. If looking for free software that is very good take a peek at Darktable, rawtherapee, Krita, and for the very complex photoshop-esque level "The GIMP". Open source pleases my Linux bigot nature, although I have and use Windows machines for the apps I want that have no open source or Linux native equivalents. Pragmatism beats dogma in my world.
Doing math proofs and solving math puzzles is claimed to be good for the brain. There are always new ones popping up on youtube, I take a pass at solving them a few times a week before watching the solution. Don't always get the answer myself, but rediscover rules and methods forgotten over the 45+ years since last in a math classroom. Doesn't meet your problem solving avoidance, but perhaps it's not problem solving so much as shop problem solving all the time that gets old. I'd hate to do math for hours every day, but enjoy it now and them.
Cooking is something I really like, Trying a new recipe and style is sort of fun. Never appreciated all the unexplored ingredients that are out there, or how easy many of them are to get. In a rural area Amazon is a real help, our nearest World Market is around 50 miles away. I never had much exposure to Korean cooking but have made some recipes gathered from the Aaron and Claire channel on Youtube. Aaron does all sorts of Asian cooking, I've followed along on Chinese, Japanese, and Korean recipes. Even for a first timer the results are at least decent, some are actually impressive. Souped Up Cooking is another youtube channel that has good info. Helpful hint: Use only Royal or Nishiki rice. Nishiki may or may not be easy to get depending on your grocery stores and location, but Walmart has Royal. The huge difference in quality and flavor is worth the added cost. Lesser brands these days are full of broken grains that turn to mush frequently.
Dgjohnsonstein comments on Astronomy. If that sort of tickles your fancy, a free program "Stellarium" is available for most platforms including Android. It's a bit easier than the old school juggling of star charts. Add in a reasonably good pair of binoculars and hopefully access to a darker than urban night area and wonders await.