I’m sure it’s been said, but you also want to feel around for anything warm, especially under the dash.

It appears to have been the alternator. To sum things up, my '89 Diplomat AHB had a 60 milliamp draw, and it wouldn't start after sitting couple weeks. I went through pulling every fuse, draw didn't change. Disconnected alternator, let car sit, battery stayed fully charged. Wanted to use voltmeter with alternator disconnected, but the batteries in meter leaked out and ruined it. Ordered another from Amazon. While waiting, I installed another alternator I had, slightly used but from another Dip Police car so perfect match. Left it connect along with battery for a week. Threw charger on battery, and it was fully charged. New voltmeter arrived, and it shows 140 milliamp draw! WTH?! Yes, it was on right settings, I confirmed. Doesn't make sense! Battery would have gone dead in a week with that kind of draw. It was almost dead with the 60 milliamp draw after that long.

Drove the car around for quite awhile last night, so headlights on of course, plenty of brake lights, radio on, other accessories. Came home, threw the charger on battery, and it was fully charged. I think I got a bad voltmeter. Probably Chinese junk. It was only $15 but had good reviews. Maybe some were fake. All seems well now. Btw, the bad alternator never got warm.

Story - My not too smart sister bought a 1983 Renault Fuego new. Around 86/87, in cold weather the battery would be completely dead in the morning. Not very good mechanic charged her to replace the almost new battery. Did not fix it.

I troubleshot it to a bad diode that was shorting out in cold weather and would turn everything on the aux circuit in the middle of the night and hence dead battery in the morning. She bought it at Papa's Dodge (and others back then) and I was there buying parts and inquired about the weird alternator problem. Was told its a common issue with those cars. Seriously?

So she buys a new alternator. Starts getting warm out so problem stops and she doesn't replace the alternator. Fast forward to next winter - problem reappears. So I put the alternator in. Within days the brush assembly burns up. Can't remember if alt was still under warranty, but go back to the dealer where she bought it. No longer available. Seriously? This is now about 1987 or 1988, and they sold these cars in the USA thru 1986. No alt to be had. My dad the great machinist that he was, made a set of brush holders. Thing of beauty. Burn up in several days.

I stick a Mopar alternator and voltage regulator in it. Even made a voltage sensing circuit to interface with the Renault idiot light.

A few years later she buys a new car. I said whew - it's out of my hair. Nope - she gives the car to my other sister. Couple years later the car burns down from an electrical fire. That car was an utter POS............ That was not the only electrical issue I had to deal with in that car. Plus many other issues.

What battery model is that?

something that looks odd in your picture is the terminal ends.
it has to do with the space, or lack thereof, between the ears of the cable ends.
knowing a person only needs to tighten the terminals snugly so they don't rotate, i have found terminals that do not have at least 1/8" gap between the ears have a tendency to not contact the post surface entirely, allowing air space [however minutely] between the terminal and post to possibly create corrosion in the future.
also, the negative post looks to be sitting somewhat proud of the post top. using a set of battery terminal spreading pliers would help the fit of that.
not trying to nit pic, just observing a couple of things that have caused me corrosion issues over the years.

I assume you will need a special battery charger?

don't do like my brother did one time.
he bought a new battery for [i don't remember what].
the one cable didn't go down far enough, so he [GUESS WHAT ? ] pounds on it with a hammer, thereby "kinda" sinking the post into the battery, breaking the case along the way.
he took it back to the store and told them "i don't know what happened ?"...........
when he got back with the "new" new battery, i introduced him to the battery spreading tool...............
every now and then, that story pops up between us.