Does the imam’s room or office come under the same rulings as the mosque and should one pray tahiyyat al-masjid in it?

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Check below answers in case you are looking for other related questions:
Ruling on observing i‘tikaaf in a room that is separate from the mosque
I’tikaaf in a room inside the mosque

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Related Answers:
Ruling on staying overnight in the mosque and teaching children and feeding them there
Does the multiplied reward for prayers apply only to the mosque of the Ka’bah or does it include the entire Haram (sanctuary)?
Should women be prevented from taking their children to the mosque?
Ruling on observing i‘tikaaf in a room that is separate from the mosque
I’tikaaf in a room inside the mosque

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