If you've got 5 extra nights beyond the 7 on the boat, and you are allocating them 3-1-1 in the cities you named, then there is no time for anything else (such as the Mosel River, Burg Eltz, or other places I posted in my most recent post.) There is also very little time for Mainz or Nuremberg.
You begin "Tag 8" at 9:00 am as you step off the boat. I am guessing you did not see all that much of Mainz on the afternoon prior. So you can move on from there right away, or if you wish to park your bags at the station and spend a few hours on the sights you might have missed, or on Johannisfest, that seems a good option.
Whether you linger in Mainz or you move on right away, I suggest returning as you came by train in the direction of Amsterdam to a Rhine base town for "Nacht 8 & Nacht 9." There are some things you have missed. The business of traveling to Nuremberg for one night and then flying from Nuremberg to Amsterdam would be folly, IMHO.
"The fortresses Katz und Maus (cat and mouse) in St. Goarshausen on the other side of the Rhine are also worth visiting."
Sorry, this bit is nonsense. There is no public access to either of these castles.
"You will pass the romantic fortess Marksburg, the only hilltop castle of middle Rhine which has never been destroyed"
Because your bike journey south along the Rhine appears to follow the river on the Boppard/St Goar side, you will only be viewing Marksburg from the opposite river bank. And if there is one must-see / must-tour castle on the Rhine River, it is indeed Marksburg, just south of Koblenz in Braubach.
https://www.deutschland-luftaufnahmen.de/wp-content/uploads/2020/10/Marksburg.jpg
https://www.marksburg.de/en/circuit/#/
So my suggestion for Tag 8 (presumably Sa June 21) is to catch one of the direct northbound trains from Mainz to BOPPARD for 2 nights there. From Boppard there are multiple ways of getting to Braubach, where Marksburg is located. And Boppard is just a good place to stay... many hotel and restaurant choices, some right on the waterfront promenade.
Arrival at Boppard at 11-12:00? Drop bags at hotel, see town, take the chairlift ride and the walking path at the top to Gedeonseck Terrace for a terrific view of the river valley.
Arrival at Boppard late in the day? See what you can and find dinner.
Tag 9, June 22: See town and do the chairlift if you didn't already, then head to Braubach/Marksburg in the afternoon. Done with Boppard already? You might want to catch a train to Remagen (NW of Koblenz) for the WW II museum there...
https://bruecke-remagen.de/?setlang=en
Then train to Braubach for Marksburg in the afternoon, then back to Boppard.
Braubach, btw, is a very attractive old-world town worth a walk-through and/or a meal:
https://farm5.staticflickr.com/4143/4751924826_98980aa49f_o.jpg
You should be able to find Boppard, Braubach, Remagen and Koblenz on the railway schematic below:
https://www.vrminfo.de/fileadmin/data_vrminfo/PDF/Gaesteticket/Infoflyer_Gaesteticket_englisch_2022.pdfSCj
At the end of all this, catch a train from Boppard to Schiphol airport on the 23rd (roughly 5.5 hours.)