席 and 場所: a seat and a place for luggage or meeting
Compare a window seat with space for luggage and a meeting point, without translating every 場所 as a seat.
A place for someone to sit
席, read せき, here means seat. 窓側の席に座りました。 says that someone sat in a window-side seat.
席から立ち上がりました。 says that someone stood up from their seat. Standing up does not itself establish that they left the room.
A position for objects or activities
場所, read ばしょ, broadly names a place for an object or activity. 荷物を置く場所を決めました。 says that someone chose a place to put luggage.
待ち合わせの場所は噴水の前です。 says that the meeting place is in front of the fountain. It does not specify a chair or seat.
A seat and other places with different roles
座る席は決まりましたが、集合場所はまだ決まっていません。 says that the seat has been decided, but the gathering place is not yet decided. Separate the roles of these two places.
荷物を置く場所 can include empty floor space. Replacing 場所 with 席 may instead indicate a person’s seat, so the two words are not interchangeable in every context.
Does 荷物を置く場所 necessarily mean a chair or seat for a person?
Show the answer and why
No. It is somewhere to put luggage and could be empty floor space. A role as someone’s seat is not stated.