I can't install the hp laserjet 1018 MacBook m3 Sequoia 15.0.1 printer

The HP LaserJet 1018 was manufactured in 2006 and sold for approximately $129.00 USD. I think you got your money's worth. Time to recycle the printer and buy a new one. I sincerely doubt neither HP nor Apple are going to expend any effort on supporting a printer that is nearly 20 years old.

The HP LaserJet M209d (USB only) is close in both size, specs, & price. It is more than twice the speed of the 1018. The HP LaserJet 4001dn adds Ethernet and more speed. The HP LaserJet M234dw adds WiFi, Ethernet, & Scanning.

Check System Settings>Privacy & Security>Local Network and see if it's enabled.

Yes, that is a good question. HP would probably be the key. Unless another user here can suggest a solution, you may (at least temporarily) have to use the 1018 printer with a Windows computer, or an older Mac, and print from transferred PDF files. Another (experimental) way could possibly be to use a Raspberry Pi running Linux as a print server for the USB-connected 1018, for AirPrint-like printing from a modern Mac.

There were similar difficulties with a previous printer driver package and installer four years ago when macOS 11 Big Sur was new. Various workarounds (including extracting drivers) were suggested. After a while, an updated HP printer software package was made available for download from Apple. The 1022 driver could then be used even for a 1018. I do not know what the reason for the present situation is. Could it possibly have something to do with the printer manufacturer and certificates?

HP driver not available for Mac OS Sequoi… - Apple Community

You can see if this still works

HP Printer Drivers v5.1 for macOS v. 12.0… - Apple Community

details are here

https://forums.macrumors.com/threads/monterrey-and-hp-printers.2319676/?post=30525559#post-30525559

It has to have Airprint on it to work wirelessly. From what I saw and you probably already know is that it only works on Windows and Linux

You should ask HP about that.