Is it critical to use the exact oil?
I'd be asking some current oil manufacturers, like Shell, Castrol, Penrite.
Penrite have a great reputation and I have heard many times (on a classic car forum) that they have a really helpful technical department.
I have done a bit of googling for you, looking for equivalents to your list in the post above. I got a bit of info when searching for "carnea 69 oil equivalent."
It seems there is an equivalent modern Shell product, Shell Morlina S2 B 150. It seems to be available in 44 gallon drums for thousands of dollars each! EEK.
It also lists a generic match, Vitrea Oil 150 as a specification.
I have done a bit more searching and it seems this is a very basic, low cost machine oil, in other words, nothing special.
That's why I'd contact a company like Penrite's technical advice department, tell them what you are doing, and ask their advice. I suspect that many modern oils, including automotive engine oils and gear oils, will do what you need and be a way better product that what was used originally in your washing machine.
One thing to watch is if there are any bronze bushes/bearings in the transmission, then the oil company needs to know about this. I understand that modern car gear oils (used in manual car transmissions) have additives that destroy phosphor-bronze bushes. This is a problem for old (1960s) Peugeot worm-drive differentials, which have bronze bushes in them. From the photos above I think I can see a bronze bush in your transmission.
I have now just found this...
https://penriteoil.com.au/forums/to.../Marine gear oil safe on bronze bushes?page=1
Which again makes me suggest - talk to Penrite.