If I'm working 1099 as a telehealth employee, would I be able to write off the purchase of a laptop since it's required and not reimbursed/offered via the company.

If you are a self-employed independent contractor who will receive a Form 1099-NEC from your client for income in 2023 then you can enter the laptop as a self-employment expense.  If the laptop cost was $2,500 or less it can be entered as an expense on Schedule C, but only the percentage of business use can be expensed.

However, if you receive pay stubs from the employer showing Social Security and Medicare taxes being withheld from your wages then you are an employee who will receive a W-2.  Employee business expenses are not deductible on a federal tax return due to the tax code changes in effect for tax years 2018 thru 2025.

Consider depreciation.

There are various depreciation schedules allowed for computer equipment.

Choose the one that works best for you.

@dgomez94