The 10 minutes is actual playing time. So as JH mentioned you can allow more time for delays.
The time for the sin bin includes any stoppage time. It is not "actual playing time" and referees cannot extend the sin bin to make up for game delays.
Suppose player Red 10 is temporarily dismissed at 9:00.
At 11:00 1 minute is needed to find a replacement ball and at 16:00 2 minutes are needed to treat injury. The first half will be extended by 3 minutes.
Red 10 may be called back from their sin bin at 19:00. The referee should not delay the player's return until 22:00 to make up for the stoppages during the sin bin (indeed, must not do so, in law).
Suppose player Blue 6 is temporarily dismissed at 39:00 in the same first half. No further excess stoppages of play occur.
Blue 6 will serve 6 minutes during regular time and 3 minutes during additional time. They have served 9 minutes when halftime is called.
They must remain in the sin bin for a further 1 minute at the start of the second half, after which they may be called back.
Modifications to the Laws said:
The referee must include in the temporary dismissal period any time 'lost' for a stoppage for which [added time will be given]