First of all, it wasn't "Biden’s law". It was a proposed regulation under a existing law passed by Congress, specifically the Occupational Health and Safety Act. The suit challenges whether the act properly authorizes the regulation, and whether if it does, the regulation is constitutional. The Fifth Circuit has not yet come to a decision on either point.
Until the court issues a decision or lifts the hold, the regulation cannot be put into effect. Until then, the law is as it was before, that being:
Any employer may impose vaccine requirements if it so chooses, unless a valid state law prohibits this. If it does, it must allow for "reasonable accommodations" for those who have disability issues (under the ADA) and for those who have sincere religious issues with compliance. Any accommodation mu7st serve the "business need" that the employer had in mind. If no accommodation will serve the need, the employer does not have to make any accommodation.
The employer may make vaccine receipt mandatory for all employees who enter its workplace, or for certain types of employees, such as customer facing employees. It may, but need not, offer frequent testing as an alternative. It must provide reasonable accommodation for employees with a disability or a religious objection, but may choose what accommodation(s) to offer, and need not accept one proposed by the employee, provided that it offers at least one "reasonable" accommodation. What is reasonable depends on the individual specifics of the situation. If an employee does not comply and does not qualify for an accommodation, or will not accept an offered accommodation, the company may, if it chooses, discharge the employee. All this is unchanged.
The regulation, which was scheduled to go into effect in January 2022, as I understand it, would have required employers with over 100 employees at a site to mandate vaccination or frequent testing. That requirement will not apply until the regulation is implemented, if it eventually is.