Pillar 2a, what happens when I leave CH?

If I leave Switzerland for another country what happens to my Pillar 2a? I’ve heard that it gets transferred to a bank account and that I earn no interest in it. Is this true? Is it possible to transfer it to some company like Finpension or VIAC that allows me to invest my money however I want?

Also when I take the money out of Pillar 2, do you know if I will be taxed in my new country (EU)? Is there an EU-wide rule ?

Hi, search “vested benefits” in the forum as it has been discussed mutliple times

Yes

Depends on Dual Tax Agreement with Switzerland which is per country NOT EU wide. Discussed here for example

You have to instruct your pension fund where to transfer your benefits to.
If you don‘t, I‘ll open up a vested benefits account for you.

No, virtually all vested benefits accounts pay interest (or allow for other investments).

Probably, yes. Though as @Barto already, said, depends on the applicable DTA. I assume most countries do tax the payout (especially after Brexit).