Persistent bootloop following battery replacement - need advice/help?

I was wondering if anyone could provide me with some advise on this or at least better background knowledge on the topic.

My iPhone SE was starting to have issues due to an old battery (typical issues like overheating up, non-responsive screen, and occasional shut-downs; ~550 charge cycles at that point) so after doing some research I decided to replace the battery.

I had planned on doing it myself and getting a battery from here (I’ve done other things like replacing my HDD with an SDD in my MacBook, etc.) But I’m working/living away from home and I don’t have a great workspace, so I decided to not risk it and brought it into a repair shop - no Apple Stores anywhere nearby and it would be way overpriced without warranty anyhow.

BUT now my phone is almost constantly boot-looping and the screen flickers. No specific “processes” seem to be causing it (iCloud maybe? but it crashes with calls, texts, google calendar, etc) and it’s getting progressively worse. It will get stuck for hours. Sometimes it will go to lock screen, but when I unlock it goes immediately into a bootloop again.

I can’t shut it off or put it in “safe mode” (if that’s even a thing anymore - never got it to work on my phone) when this happens. I’ve noticed that if I attach it to a power source it will stop and run. It will still bootloop, but less often.

From what I’ve read these issues typically indicate:

(a) faulty battery and/or damage during replacement OR (b) software problems

I think it’s option (a), because ..

• It started bootlooping either the same or next day after the battery was replaced.
• It tends to stop, if it’s plugged into a power source.
• Bootlooping gets worse under 80% charge (As an aside, it will flash 1% battery if it bootloops and then returns to lock screen… might just because “my phone is having a toddler moment”?)
• I restored my iPhone to a “clean” backup to check for corruption in files, but bootloop is still happening, unless a corrupt file wasn’t overwritten. (Note: *I didn’t upgrade, because I need specific apps for my job and some other things, that won’t work with the newer iOS, so updating to newer iOS is a non-option and it’s probably why I’ll abandon Apple - happens way too often)
• And … I was a bit worried because when I dropped off the phone, because one of the guys said “the SE uses the same battery as the 5S right?” and he was told “no, but there should be some SE batteries somewhere in the back”. I told myself that it was fine, because everyone has to start somewhere and he did ask … BUT at the same time, I even knew the answer to that question and I don’t even work in electronics.
• I’ve also managed to pull an error from the iPhone console that says “trigger com.apple.duetactivityscheduler.batterylevelpolicy.batterylevelchange because conditions are deteriorating” - not exactly sure of that code though

I am going to go back and talk to them, but I want to be knowledgeable enough before I go in and question the battery situation. Like I said, I don’t think it’s the iOS, but they might argue that? It’s a big coincidence that the bootlooping started when the battery was replaced.

I don’t want to sound like an idiot and I really can’t afford a new or even used phone at the moment, so I’d like to fix the issue one way or another. Should I take a look and see the situation before I go in? Is there a good way to ID a battery that is bad in addition to pucking/swelling. What would happen if he had used a 5S by mistake, is there a good way to identify this - model #, etc?