Thanks for the clarification.

For anyone wondering, the story is a little more muddy:

Old Frisian burich “castle, city,” Old Norse borg “wall, castle,” Old High German burg, buruc “fortified place, citadel,” German Burg “castle,” Gothic baurgs “city”), which Watkins derives from from PIE root *bhergh- (2) “high,” with derivatives referring to hills, hill forts, and fortified elevations.

In German and Old Norse, chiefly as “fortress, castle;” in Gothic, “town, civic community.”

https://www.etymonline.com/word/burg