In general, unemployment is not considered a public charge for the new public charge rule. However it may be seen as a negative factor if you apply for a visa in the future.
As a visa holder, Am I eligible for unemployment benefits?
Some visa holders are eligible for unemployment while others are not.
If you are the principal visa holder ofE-2, L-1, H-1B, O-1, among others, you may not be eligible for unemployment benefits. The main reason being that a person needs to be readily available to accept employment when requesting the benefit and these visas restrict employment to the sponsoring employer.
However, immigrants holding a valid employment authorization (EAD) have no restriction to work, thus are eligible for unemployment benefits. Example are spouses of E-2 or L-1 visa holder, F-1 students with OPT. However, if the EAD is expired the person is no longer eligible for unemployment.
Note that aside the immigration status, the person must meet all other unemployment application criteria, which usually differs from state to state.
Click here for information on how to apply for unemployment benefits in Florida.
 Public charge fact sheet https://www.uscis.gov/news/fact-sheets/public-charge-fact-sheet