Hi Lydie,
There is no import tax for ETF shares. In fact, you can keep your securities at your foreign broker after moving to Switzerland if you choose to. From a tax perspective it makes little difference whether your securities are managed by a Swiss or foreign broker, except that Swiss brokers have to levy Swiss stamp duties, and foreign brokers do not. You can find more about that in this Moneyland article:
https://www.moneyland.ch/en/foreign-vs-swiss-stock-brokers-online-trading
Personally I would recommend that you keep your euro-denominated ETFs at a low-cost European stock broker after moving to Switzerland, and use a Swiss brokerage account for CHF-denominated ETFs and/or for assets which you want to keep in Switzerland (for geographical diversification).
In today's world where securities are generally in book form only without stock certificates, "transferring" securities generally works like this: Your old broker sells your securities, and your new broker buys identical securities. The old broker informs your new broker about the time at which they will sell, and your new broker buys at the same time so that the price is more or less identical. Brokers generally charge for this service, so you need to consider whether it makes sense. In some cases, your new broker will cover the fees charged by your old broker for this transfer service.
In short, don't worry about it. Moving to Switzerland will not affect your existing investments. You will not pay special taxes due to moving. Moving to Switzerland may benefit you with regards to your ETF investments because Switzerland does not tax private investors on capital gains. You can find more info on that in this Moneyland article:
https://www.moneyland.ch/en/stock-market-profits-tax-free
Best regards
