The best way to keep the list of options the same across the two tables is to use a linked record field that links to the same table.
For example, have a “hard skills” table with the list of hard skills. Then have both the USER and PROJECT tables link to the “hard skills” table. When you add a hard skill to the table, it will show up as an option in both of the other tables.
If you prefer the look and feel of a single select or multi-select field you will need a manual workflow that ensures you keep both in sync. There are some manual workflows that involve code that can make the process easier. For example, you could have a script that creates the option in both fields in both tables. But you still need to manually run the script.