Must this adversary (or any data collector) be watching me live, exactly to the time point, if I would make the swap with ETH?
No, not at all. Given that both Bitcoin's and Ethereum's blockchains are completely public, anyone can look back at any point in the future and try to link your transactions together. Hence why you would want to use Monero.
And if at that time point there was no data collecting and I have moved the ETH around, waited as long as possible before swapping back,
then in retrospect it would be the same with ETH like Monero?
Again, no. Since Ethereum is public, then simply moving coins around a bit is easily tracked, which again is another reason to use Monero, since such movements cannot be tracked.
But as above, given how complications this is, and the many potential pitfalls, most people just opt to use a mixer instead.