Besides the advice from @MartinR, you have several other options.
The easiest method would be to create a new spare/dummy macOS admin user on the new Mac....don't associate your AppleID/iCloud with it. Then use Migration Assistant to migrate your old Standard user account to the new Mac. It is critical you only migrate the macOS user account and none of the applications or system wide settings since they won't be compatible with the new Mac. Once migration has completed, you can use the spare/dummy admin user account to elevate your old Standard user account to an admin user account on the new Mac. The main downside of this approach is the new concept of "Ownership" with the new M-series Macs. While all admin user accounts should be equal, it is possible the first created admin user account may have some special meaning to the M-series Mac (this is not 100% clear if there is a difference, just something to keep in mind).
You can also use a Time Machine backup of the old system here as well.....I think migrating from a TM backup would be the best option for the above since it would probably prove more reliable depending on the amount of data involved. After successfully getting your new Mac up & running, you can then erase that TM backup drive (assuming you only created it for this migration) so you can start a fresh new TM backup for your new Mac.
Back up your Mac with Time Machine - Apple Support
Another option would be to create a new admin user account on the old Mac, but this involves using the command line. This new admin user could then elevate your original macOS user account to an admin user. While a respected forum contributor created an article with the instructions to create a new admin user.....that article is meant for macOS 10.15-14.x. Someone familiar with the command line could easily use it as a guide for High Sierra. I have made several posts on this forum many years ago with the instructions that are compatible with High Sierra, but don't have the time at the moment to search for those posts. If I remember, I can try to locate them later today or I may just write a new set of instructions. The option to create a new admin user on the old Mac & upgrading your existing user from Standard to Admin would allow you to transfer that user account to the new Mac....since it is the only user account on the new Mac, that transferred user will be considered the "owner" so it should minimize any "ownership" issues from my first suggestion.
FYI, using Setup Assistant or Migration Assistant even from a TM backup may have some difficulties because you are moving from a very old OS to the current macOS 26.x Tahoe which is a huge jump and many things have changed even when migrating just the macOS user account. Even manually migrating can be problematic especially for music, photo, & video libraries since those libraries & associated apps have changed. Migrating just the data is not a problem (Desktop, Documents, Downloads). Just something to keep in mind.
Another tip would be to avoid signing into your AppleID or iCloud until after you have completed setup of your new Mac. Besides slowing the Mac down while syncing any data with the cloud, there has been a known bug where a user is unable to agree to the new Terms & Conditions of the new OS while logged into an AppleID/iCloud.
If anything goes wrong while setting up your new Mac.....it is very easy to reset the new Mac to factory defaults by deleting any broken migration or configuration by using the "Erase All Content & Settings" (new feature) which will put the new Mac back to factory settings & running Setup Assistant again giving you another chance to set things up differently. This process is very quick.
FYI, you definitely want to have frequent and regular backups of your new Mac and all external media (including the cloud) which contains important & unique data. There are a lot more new ways to permanently lose access to the data stored on the internal SSD of the recent Macs due to all of the hardware, software, and security changes. There is very little hope of recovering any data if something goes wrong unless you have good backups.
I know this is a lot to take in, but these are your best options along with @MartinR's suggestion to manually transfer your data.
