Same problem to install and setup this printer hp p1102w BUT I did get it to work finally...
HP website is hard to use and does not seem to work. Here's the page for drivers for win 10: https://support.hp.com/us-en/drivers/selfservice/hp-laserjet-pro-p1102-printer-series/4110394/model/4110306
As noted above this is the main driver link? https://ftp.hp.com/pub/softlib/software13/COL32431/bi-80329-12/hp_LJP1100_P1560_P1600_Full_Solution-v20180815-50157037_1.exe
But I could not get it to work...
There is also a utility called HP Print & Scan doctor so I tried that. Again I could not download from HP but if you google it you can find other download sites.
It took a while to install and then to find my printer on the network but after several tries it did find it and INSTALL it successfully. I just printed on it so I can verify that it works!
So YES it is possible to get this printer working in Windows 11. Neither HP nor Microsoft seem to want to help you to do this, but it can be done!
You may read elsewhere that this printer is "not" compatible: https://answers.microsoft.com/en-us/windows/forum/all/i-cant-install-driver-for-hp-lj-p1102-in-windows/5713dd89-9066-4a70-8af5-0ebbef8d4840
Whatever that means... but it is possible to use the printer using (I presume) the win 10 drivers.
Don't listen to HP or MS telling you it is not possible, because it is. Good luck!