@Katherine956,
Hi, Airbnb is a short term rental platform and what you are asking does not currently exist on their platform (background check and long term lease contract).
I’ve known other people who do a background check on their own through a different platform, have the guests sign a lease (for cities that require it for stays over 28 days and to protect you as a landlord as different rules apply for short term vs long term renters - long term renters have tenant rights), and even collect a deposit through a third party website (for longer stays and/or large home rentals).
I know some platforms like Zillow provides background checks as part of the service when you list with them but Zillow is a long term renting platform. That said, Airbnb will bill the guest monthly for longer stays and you will get paid monthly as a host. We had a 2 month guest once and got paid a few days after the day after check in (I have it set up for bank ACH deposit) and one month later on the same day.
There are some websites designed for landlord forms and support that you could check out too. One did background checks and provided forms (it had forms specific for all states in the US) for a small fee or pay a monthly subscription for more benefits.