Is my transmission failing?

Background: My car is about 7 years and 1 month old, and I have been driving it for 4 years daily. When I bought the car used, it had 18,200 miles on it. It now has 160,350 miles.

[Recent part replacements/cleaning:
- new battery
- new alternator
- new air filter
- regular oil changes every 3k miles
- cleaned throttle body
- topped off coolant
- added Gumout fuel system cleaner
- new brakes recently, new calipers months ago]

[Current issues that need attention:
- worn suspension parts
- feathered tires
- drive belt system, loose tensioner and frayed belts
- needs coolant flush
- needs brake fluid flush
- needs right control arm and bushings
- possible oil leak but very small
- black liquid speckles on brake line, spraying out from somewhere]

The problem I'm dealing with and asking about:

I'm noticing a relatively new problem with the way the car drives, and it began around August 2022. It is getting worse. The first problem I noticed was slow/loud acceleration. This tended to occur while driving uphill, and I could hear/feel a vibration that rumbled the whole car as I accelerated. Now this occurs on any level surface as long as the RPMs are low.

Accompanying this is a strange clink sound that I hear when moving from stop to drive, and it happens in reverse as well. It sounds like someone tapping the side of a tin can with a spoon. It only occurs when moving from a halt.

As of about two weeks ago I noticed the car vibrating when in reverse. It makes a similar sound to the rumbling I mentioned earlier. The acceleration is also very weak, and I can feel a thud when the car shifts from first to second gear, and vice versa. It's very jerky.

The gears do not slip, however. There is no problem moving the shift knob and it does not change gears once I move it. It just feels generally weak and bumpy. Is this a potential transmission problem? Maybe a torque converter or mount?

One other thing to point out that is very unusual: This only occurs when driving downhill and applying brakes. My RPM will shoot up as if it's trying to shift up, even though I'm slowing down. Sometimes the problem persists if I eventually brake to a stop. It will sound like I'm slowly pressing the gas pedal down.

[Currently there is NONE of:
- smoke coming out of exhaust or engine bay
- transmission fluid leaks
- flashing engine light (only stationary)
- auto transaxle light
- stalling at high RPM's or while the car is in motion at all
- puddles of anything under the car besides water
- problems starting the vehicle]

Other issues to note:

In the spring of 2022, I suffered a serious malfunction with the vehicle that ended up resolving on its own. The check engine light, TPMS and TRAC lights would all appear at the same time and the car would get stuck in failsafe mode. Even if I drove with the hazards on in that low RPM, the car would lurch and shudder. This seemed to resolve after about a month of not driving it, only turning it on and off.

This issue occurred much less severely every time it got cold, every single year and would go away with the warmer months.

Any help or advice you have would be greatly appreciated. I am currently waiting to start a new job, so I don't have the money to just go to a shop and get an engine evaluation.