Should a Wi-Fi router or wireless access point be installed inside the metal cabinet?

Generally, no — not if you expect its wireless performance to matter.

Most of the cabinet is steel. That is excellent when you want a strong enclosure and considerably less helpful when you put a radio transmitter inside it and ask the signal to escape.

The glass door doesn’t turn the cabinet into an RF-transparent bubble either. Some signal may get out, depending on the antenna position and surroundings, but you’re deliberately making the wireless environment harder.

If a router also performs useful wired routing duties, there may be perfectly good reasons for the router itself to live in the cabinet. Where practical, put the wireless access point or antennas outside the metal enclosure.

Otherwise it’s quite possible to lock an access point neatly inside the rack and later install another access point to cure the coverage problem created by the first one.