hotel in the Alps (zillertal)

I have no knowledge about this hotel

Paying 40% upfront in cash is outside my comfort zone.

If anything goes sideways you have no leverage.

Hopefully others will have better insight into this method of business or the property or both.

Some small hotels do still work like that in Austrian mountain resorts; their clientèle is mostly regional and German-speaking so it is less of an issue.
In your case, the bank transfer will cost money (not too much if you use Wise), and as rightly pointed out it offers you no protection whatsoever.
Does the hotel take credit card payment? If so, they are able to process a deposit by CC and you should ask for that. I would be much more comfortable giving my CC number to a hotel clerk by phone if needed than sending a bank transfer overseas.
If not...another hotel maybe?

It is very common in Austria to pay for things via bank transfer, as checks do not exist here. Particularly common when one person need to pay another person. I pay my rent, for example, by bank transfer. When I explain checks to Austrians, they think that is so crazy that people still do that in the US.

That said, the hotel website indicates that payment can be done with a credit card.

That said, the hotel website indicates that payment can be done with a credit card.

What I saw on their website is that the upfront 40% deposit was to be paid by 'bank transfer' and the balance due, paid on arrival, could be paid by select credit cards

If you have a PayPal account then you can sign up for Xoom - a PayPal subsidiary - which allows you to transfer money from your PayPal account to any ordinary bank account in another country.

I have paid a deposit to small Bavarian and Austrian establishments in the pre-COVID past via bank transfer. It is not terribly unusual for businesses there to ask for this. It is not a deal breaker for me, but I usually stay at inexpensive establishments (which this hotel appears to be), so it is no big deal to me.

I made inquiries to about more than 30 small inns and farmstays in Austria last year. Most do not take credit cards and mandate a wire transfer for deposit. It's very common. As mentioned above, use Xoom from Paypal. It's fast and reliable.