iMac running slow all of sudden

Either the hard drive is failing or you have some third party software installed which is causing problems.

Try running the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics rarely detect issues.

Try booting into Safe Mode. If Safe Mode works, or works better, then run EtreCheck and post the report here so we can examine it for clues. Also run DriveDx (free trial period) to check the health of the internal drive(s). Post the complete DriveDx text report here using the "Additional Test" icon which looks like a piece of paper. If this iMac has a Fusion Drive, then please post the DriveDx reports for each internal drive.

The large negative numbers indicate some sort of network issue while attempting to boot into Internet Recovery Mode. Unfortunately Apple doesn't explain them or provide any descriptions. Could be a WiFi issue of some sort, or it a router issue or router configuration issue, or some other item on your network, or it could be your ISP, or even your local regional network.

Try connecting the iMac directly to the router using an Ethernet cable which will bypass any hard to troubleshoot WiFi issues.

If a direct Ethernet connection still gives you similar errors, then power cycle the router.

A failing internal hard drive with a severe drive failure can prevent the Mac from booting even from external media. It may be possible to check the health of the internal hard drive by creating & using a bootable Linux USB stick which may boot even with the drive failure (Linux is more forgiving sometimes as it will ignore or skip past some errors). If interested in instructions, let me know.