What do you do when migration assistant doesn’t finish successfully?

I did so, but the furthest that I could get it was about 1/3 done of 135 GB. It had moved some of my files, but none of the other users files. I gave up and moved the rest of my files from a backup using a file sync program. I then logged into each of the other users and manually copied their files from the backup.

Some more details here. The new machine is a M1 iMac, the old one is a 27" mid-2010 iMac. A very fine machine, but stuck on High Sierra. I attempted the transfer 3 times. The first time it told me I was going over wi-fi and the transfer would take over 4 hours. I thought that was a bad idea and canceled the transfer. I started the second transfer over ethernet which appeared to be running, when I came back about a 1/2 hour later the screen was black. Restarting the M1 iMac yielded an exclamation mark inside a circle and instructions to visit a support site. Basically the iMac needed to be re-initialized, which I could not do from my old iMac. So a trip to the local Apple store where the genius tried to perform the necessary operation 3 times. No luck, so that machine was returned and a new one ordered.

The third time with the second iMac, I was very careful to follow all of the instructions and was transferring over ethernet. Estimated time was initially 58 mins and files were merrily being transferred. However, the time estimate didn't change, when it did about 15-20 minutes in it went to an hour and a half or so. I left for a short time, came back and it had lost the connection to the old machine. After restarting the migration assistant on the old machine, it still couldn't re-establish the connection. So I aborted and posted the first message above, late at night. The next day I called Apple Support, the lady was very helpful and recommended that I transfer the files from my backup, which is what I have done and so far everything seems up and running.

Unfortunately my time machine backup was internal. The external hard drives were being used for other files. I would have had to reconfigure those files to establish an external TM. Probably almost as much effort as what I ended up doing. If I had seen your post before the third attempt, I might have done it that way. Oh well, live and learn.