HP 5.1.1 Printer Software Update - Apple Support
An HP LaserJet Professional M1130 MFP Series 1.8 was mentioned in an earlier article listing drivers in the above package. However, the text for the download says Not compatible with macOS v12 and newer, so do not expect a it to work with macOS Sequoia 15. If the package will not install, modifications have been suggested for HP LaserJet P1005 and other models (community search), but the success rate is somewhat unclear.
If a compatible HP driver for macOS 15 cannot be found, or if another software solution is not possible, you may have to look for a workaround.
Linux drivers are available for the HP LaserJet Pro M1132.
https://developers.hp.com/hp-linux-imaging-and-printing/supported_devices/index
If nothing else works, you could perhaps investigate whether an inexpensive Linux-based Raspberry Pi print server could make a USB-connected HP LaserJet Pro M1132 act as if it were an AirPrint printer, in order to allow "driverless" network printing from a modern Mac or an iPhone/iPad. This would be experimental. Details about how to set up such a Raspberry Pi print server (for another printer) can be found in the posts by Techguyuk in Can’t print with iPadOS17 - Apple Community. Tesserax reported about using a Raspberry Pi 3 Model B+ for an old HP LaserJet printer (in Can I connect my laser printer to my netw… - Apple Community).