In my experience, the common term used to denote a "Foundation" is "pratiShThAna".
The word "SaMsthAna" was used for the various "kingdoms" under the British Domain - somewhat like a State or a Province. It is also used to denote an institution in Hindi.

Allen W Thrasher wrote:

SaMsthAna is pretty common in modern Sanskrit for "foundation;" many
institutions publishing in Sanskrit include it in their name on the
Sanskrit title pages.
Allen Thrasher

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