You don't need HP drivers for the HP SCX-3405w. It is supported by Apple's built-in AirPrint service when networked (wired or wireless). In the Printers & Scanners panel, with the networked SCX-3405w powered on, you can either right-click on the device entry in the Printers listing and choose Reset print system… or simply select it and click the [-] button to remove it.
When you click the [+] button to re-add the device, a panel will appear with your detected printer via bonjour. Select that entry, and the Use: field will change from gray; auto-select will automatically appear, and then changes to AirPrint. Click Add, right-click on the SCX-3405w entry in the Printers panel, and set it to be the default printer. Done.
You should be able to use Apple's Image Capture for the scanning support on this device, and there may be additional setup on the printer's panel to do that, or luckily Image Capture will just detect it.
I just removed my Samsung ML-2955ND laser printer on macOS 11.6.7, and re-added it using the preceding steps. A subsequent test print was successful.