Follow on from the work done in T97323.
Tabbing in the template dialog now works as intended in Chrome and Safari, where you can tab to the parameter actions (info and delete) and interact with them using the spacebar and the enter key.
However, in Firefox, tabbing goes straight from one parameter field to the next, skipping the parameter actions entirely. Fixing this is low priority because it's still an improvement on the behavior before the fix in T97323 (tabbing to the parameter actions but being unable to use the keyboard to do anything useful once you were there), but it would still be good for accessibility and cross-browser standardization.