There probably aren't 50,000 Stinger missiles across all military inventories globally, never mind just Germany.
Most countries do not maintain a massive inventory of MANPADS, there is no use case for having that many. There have only been 70,000 Stinger missiles produced globally over the last 40 years and quite a few of those have been used up in various conflicts or are well past their shelf-life. Most countries with decent militaries have hundreds or thousands. Due to the shelf-life, maintenance, and obsolescence issue, it is rather expensive to stockpile a massive number of MANPADS if you don't expect to need them soon.
They don't go through them that quickly, for two reasons.
First, even advanced MANPADS like the Stinger missile have a very constrained scope of engagement, primarily helicopters and CAS aircraft in your immediate proximity due to the limited range. Situations where you can use them don't occur all that often because adversaries have a limited number of these aircraft to cover a lot of terrain. You need to be in the middle of a ground attack or staked out at an enemy airfield, and they run patrols around airfields to make sure someone with MANPADS cannot get within practical range.
Second, many wealthier western militaries expect to be able to suppress the kinds of aircraft that MANPADS are designed for with conventional Air Force and air defense assets; MANPADS are what you use when the adversary has a dominant air attack position. If the US or NATO ever finds itself in a position where some adversary has established clear air dominance or outright superiority, a great many things have gone horribly wrong. The only time MANPADS might be useful is clandestine or covert missions where there is almost no air support at all because you aren't supposed to be there.
The US maintains a large inventory of MANPADS, but mostly for situations like the Ukraine where an ally that has no ability to establish air superiority needs to suppress the ground attack assets of someone that does. Being able to airdrop a large number of MANPADS in a very short period of time is helpful in this scenario.
This stuff can be expensive. From what I can tell each stinger missile costs around $38k. So 500 of them is about $20 million worth of missiles. 50k would be $1.9 billion worth.
Germany has a strong streak of pacifism as a core Identity ever since WW2. That includes a prohibition against exporting arms into conflicts that needed to be waived here.
Yes, they will tend to err on the side of caution, even drastically so. They make up for it with lots of money and taking in a large number of refugees.
German politicians have occasionally tried a friendly approach towards Russia/the SU starting with Willy Brandt in the 60s. Those diplomatic efforts led to Gorbatschow having enough trust to dismantle the SU peacefully.
There were some business interests involved in the issue of SWIFT, mostly the fear that oil & gas deliveries will seize immediately. Beyond that, nobody believes that any meaningful trade will happen going forward. Only some drastic event, specifically the end of Putin, will allow for a reset of the relationship.
Besides, it doesn’t really matter if Germany send these arms. Germany is part of the EU, which has authority over trade, and is also seen as a block by the #russian government.
Why not 50,000? That would send a clear message of German support for Ukraine; they are already showing that with the initial delivery but…
Just curious ..why not send more?