BMW battery *rant*

i have an F33 2016 428xi that ive owned for just shy of 3 years. i want to know how cooked i am.

context: its COLD here. lately -25c some days. There are known mice at my house that go from a barn into all the cars (i dont keep food there) and the mice often set off my car alarm.

Today -25c again, i got in and got low tires, common, no issue, but when i got to work (after being home 2 days because i was sick) my car told me the battery was low. my commute is only about 8 miles.

This is NOT behaving like my 09 battery when the alternator died. nor does it say anything before or during the drive,

my plan for the issues: I just had mice traps delivered, will be adding to the floors and by the wheels at home, these mice wont last too long. im hoping that if the alarm goes off less, that the combination of the lack of alarm + it not being cold will remedy this issue.

i may replace the battery and reprogram it, im assuming at 6 years old the battery had not been replaced. so its a 9 year old battery. should this be the route i take?

questions: is there a way to see battery info in the car? i cant tell if my 30 minute drive (at lunch to troubleshoot) was just too short to charge it past the cold weather. do i need a longer time to drive if all the heaters are running? (remember im driving -25c so i have to keep warm myself)

obviously a lot at play here and a few missing info pieces, im just info dumping so i can solve the problems.

in addition my washer pump hasnt worked in 2 years so the frozen reservoir keeps telling me its empty, would this cause a drain on the battery?

EDIT: this all started happening when we crossed -10c, i have received the discharge notification a few times overnight, making me think the frozen pump / alarm are the drains. but maybe the pump is its own issue.

Update. yesterday was BRUTALLY cold, so i think the heaters in the car were pulling voltage so the commute to work was nothing (8 miles) and i drove for 30 minutes at lunch time, that wasnt enough, then i drove casually for an hour, that did nothing. THEN because of the trip i wasnt taking any risks, i drove 50 minutes to get a charger/extension cord. this last trip was the kicker, it was moderate driving 50-60mph, and my car has a monitor so i could see that once i passed 45ish mph the climate system went into "eco" and with the big hills at 60 mph when i would coast i could actually see when it was/wasnt charging the battery through the normal menus!

This last trip was enough to charge the battery so i bought the stuff and will be keeping it for a week to see what happens. last night arriving at home no issues, today no issues. i think it was brutal cold + me being sick and not traveling/ one 4 mile trip each of those days, add that to my commute not being a lot regularly and it all seems to add up to no issue but no opportunity on a normal day to charge correctly.

Thank you for your help/info.