You need to show us a photo of the keyboards before we can tell you what it is.
And no, regardless of what this is, it is not worth $2-4k, unless you fill the bellows with solid gold.
In regard to your original question on how much to offer - once we've established what this is, the picture will become clearer, but I'd be reluctant to part with anything more than $50 going by the couple of pics that you posted.
You need a photo of the insides too - without knowing the condition of the reeds, you can't put a value on the instrument, but by default assume that the reeds are completely dead and need an overhaul.
I don't know whether I disagree with what you said, but just to clarify, I did not mean to imply this instrument was worth $2k-$4k. I said a golden era bandoneons could be worth that and since Hohner was stamped on the instrument I thought it could be a good (original) quality old instrument. I don't see anything in the photos that indicated condition, and therefore made no comment about that other than the generic condition affects price statement.
All that notwithstanding I'll provide a couple of sources justify my valuation of bandoneons
https://www.libertybellows.com/shop/Concertinas/Bandoneons.htm
From
https://en.wikipedia.org/wiki/Bandoneon
"Historically, bandoneons were produced primarily in Germany[
citation needed] and never in Argentina itself, despite their popularity in that country. As a result, by the 2000s vintage bandoneons had become rare and expensive (costing around
$4,000), limiting the opportunities for prospective bandeonists. In 2014, the
National University of Lanús announced its plan to develop an affordable Argentine-made bandoneon, which it hoped to market for one-third to one-half of the cost of vintage instruments."
Also here in the Los Angeles area my teacher doesn't play them but does repair them often, said their are typically worth in the thousands.
On the contrary I do see some on eBay in the $300 range.
I thought all comments in the thread were valid probably the most insightful being Dingo40's because in the end it's "what's it worth to me" and the poster seemed to have no idea what he's in for.
I don't disagree with your or Tom's valuations, it's probably what I'd offer a random seller. But if the reason he's asking how much to offer is because he's, for example buying from a friend and wants a fair value then it's a more complicated question that probably cannot be answered on this forum.