Upgrading PG11 to PG17 without dump/restore

Hello!

There is a heavily used server, with older debian, and PG11.
The data is more than 1,2 TB.
The PG_Upgrade is not possible because of lesser space and too old debian.

As we see now we have only one way to move this server.
1.) Installing a new server with actual debian.
2.) Installing the newest PG (17) on it.
3.) Stop work on one database. Dump it in the old, restore it in the new
and start the work with that. So we can move them one by one.

But this seems to be very hard, because we need to do this through an
internet connection, and the data is too much.

I have a question about it - is there a better way to do this?

For example we make a new cluster element (a read only slave) with newest
debian/PG, and use it to move the data in the background (replication).
And then we rename it to master. But I don't know if it's possible or not.
Maybe the slaves must be the same version as the master.

The main problem is that debian is too old, and we are afraid to use
PG_Upgrade because of too many version differences (11 < 17).

But maybe you have some good advice, how to do this with less complication.
Users can tolerate short downtimes, but not longer ones.

Thank you!

Best regards
dd