Many years ago my wife surprised me with a beat up double bass that she found in the back of a store. It's a 1940's German plywood bass that sounds great
One, the instrument has sentimental value and two it sounds great. These count for something.
Well, it's going to cost something to fix, for sure, given that the neck's going to have to be done for much else to be meaningful; that old 'repair' is a disaster. Looks like the neck needs reset, you probably need a new tail wire because the tail piece placement is awful, and almost certainly the fingerboard will need redressed. Getting sound post and bridge right will kind of disappear in all of that. However, the result would be a very playable bass that will almost certainly sound dramatically better than it does now. How good, of course, you can't know without knowing more about the bass.
I think of dressing the fingerboard, along with sound post and bridge setup, as normal maintenance. The guy who works on my basses automatically replaces the tail wire on new cheap ones. So the neck reset seems to be your main worry.
There are "pure" ways of fixing the neck and there are ways that are effective but not "pure", without being a hatchet job. Specifically any use of metal screws or modern non-animal glues is, I understand frowned upon, though in the case of a cheaper bass they may make the repair cost effective.
I broke the neck off my cheap plywood bass about a year ago and was faced with the following choices:
1. Install new good neck - approx $3,000
2. Install new neck same quality as bass - $1,000
3. Bolt and glue old neck together using modern glues - $280.
The bass was worth maybe $1,000-1,500. (These are Australian prices. US prices are usually much lower I think). Option 1 wasn't worth it, and my repair guy's advice was that option 3 was considered cheating by purists, but in his view would result in a stronger neck than option 2. No complaints with the repair so far.
So when a luthier advises repair, it's probably worth asking how they will approach it. There might be better and cheaper options. In New York I would also imagine you could approach a couple of luthiers for advice. Not possible here.
(Of course, if the bass is collectable, I would spend the money to do a proper job!)