With Silicon Valley Bank’s future uncertain, startups backed by venture capital looking for new lenders are facing higher borrowing costs, onerous terms or even closed doors, potentially throttling their growth.  

Artificial-intelligence startup Artifact has hit a wall trying to secure credit from several large banks, said co-founder and Chief Executive Nate Sanders. The Salt Lake City startup began looking for alternatives for its multimillion-dollar venture-debt facility with SVB when the bank collapsed earlier this month,…