Tender (the verb) just means to “present something for acceptance”, but it’s one of those words that only survives in a few expressions. Nobody really uses it generally any more.
But another common expression in which it is used is a tender offer (which itself is rather redundant.)
ETA: And of course there is the related noun which is printed on all our money: tender is anything presented to satisfy a debt.
Tender is in regular use in British English in relation to public procurement - a government agency announces a contract that it wishes to enter into; interested parties submit tenders; the agency chooses the most attractive tender and a contract is formed with the successful tenderer.
You tender payment of a debt. If you’re sued on a debt, it’s generally a defence to show that you tendered payment and it was declined. It’s in this context that it matters whether banknotes are “legal tender” or not.
This is what I was going to add. Very much common usage in Australia, not just government departments, but companies also will seek tenders for specific contracts or services. Being in the banking industry, I often see large businesses seeking tenders for their banking requirements.