MySQL: update a field only if condition is met

Another solution which, in my opinion, is easier to read would be:

UPDATE test 
    SET something = 1, field = IF(condition is true, 1, field) 
    WHERE id = 123

What this does is set 'field' to 1 (like OP used as example) if the condition is met and use the current value of 'field' if not met. Using the previous value is the same as not changing, so there you go.

Yes!

Here you have another example:

UPDATE prices
SET final_price= CASE
   WHEN currency=1 THEN 0.81*final_price
   ELSE final_price
END

This works because MySQL doesn't update the row, if there is no change, as mentioned in docs:

If you set a column to the value it currently has, MySQL notices this and does not update it.