I would add a new text field specifying the max length as the default 256. Then run a calculate field to map the old string across, delete the old field and rename the newly created one.
If you have access to the feature class on the database level.
My dataset is not versioned and in Oracle SDE.
You first turn off all services reading using that feature class.
If someone else has
Add it to Pro and use Design > Fields and you can increase the value of a String Field. Hit save.
I have used Davids Method many times with success. Other than I rename the old field to keep it for a little.
I then rename the new field and make sure everything is working. But if your services are just referencing the text field it is not that big a deal.