There are lots of chains with the word "Relais;" I don't know what you
mean.
I think "relais" is just an old French word for "hotel". We have seen many hotels in various countries- especially France and Italy that include this word in their name. I don't think it's an actual chain or group at all.
The Palazzo Januzzi looks very nice but it is right on Piazza Tasso so expect it to be very noisy and busy- foot and car traffic. I would look for somewhere not so much in the thick of the action, etc.
We stayed at Diamond Suites this last trip- very nice, no bkft but there is a cafe right next door with delicious bkft and several other cafes nearby- it is set back off the main drag so very quiet/private. Our balcony at back of building had a little peek of a sea view. 5 min walk to Piazza Tasso and about 5 min to train station.
https://www.diamondsuite.it/en/
Another very nice hotel in Sorrento
https://www.hotelantichemura.com/
Amalfi- we have enjoyed 2 stays at Hotel Bussola- beautiful rooms and common areas, balconies with sea views, on the water level so just steps from town, ferry, bus. The staff is exceptionally helpful and friendly. The roof terrace bar is lovely- serves a fantastic spritz and really good apertivo snacks. Good bkft. We ate at their restaurant last month and liked it very much.
https://www.labussolahotel.it/en/our-hotel/