I can't imagine you would have any issues getting approved for the auto. As long as you history on those accounts are good. If you apply and are not for some reason, usually multiple inquiries within 30 days for the same purpose (all auto applications) will impact your Fico as one.
August 28, 2023 FICO 8 August 28, 2023 FICO BankCard 8 August 28, 2023 FICO Auto 8