預かる and 借りる: keeping an item and borrowing it for use
Compare keeping someone else's property with borrowing it to use. Possession alone does not establish the purpose of borrowing.
Keeping an entrusted item
預かる, read あずかる, means keep or look after. 受付では大きな荷物を無料で預かる。 says that the reception desk keeps large bags free of charge.
The notice concerns keeping the bags. 無料 is a condition of this reception notice, not a rule for every safekeeping arrangement.
Borrowing to use an item
借りる, read かりる, means borrow. 雨が降ったので友人に傘を借りました。 says that someone borrowed an umbrella from a friend because it rained.
Borrowing is a completed action here. Read the purpose of using the borrowed item rather than only the shared fact of possessing someone else's property.
Possession does not choose the verb
Borrowing a travel book at a library is a context of obtaining it for use. Its purpose differs from the reception desk's safekeeping of bags.
Holding an item does not by itself tell whether it is entrusted or borrowed. Compare management and use purposes instead of repeating a subject-direction exercise for 預かる and 預ける.
Does a reception notice saying it 預かる large bags establish that it 借りる them for use?
Show the answer and why
No. The notice describes keeping the bags. Borrowing them for use would require separate purpose information.