You can e-file for 2021. Since your wife did not change her visa status until August, she will have met the Substantial Presence Test on her own (over 183 days of Substantial presence in 2021, not to mention 2020 and 2019). No special election is needed.
However, if she is on F1 visa for the whole of 2022, next year you will (probably) want to paper-file the return. Since she will have an exempt status for the Substantial Presence test, none of her days will count, which means that, on her own, she will revert back to being considered a Nonresident Alien for tax filing purposes. But since you are a resident for tax-filing purposes, you can make an election for your wife to be treated as a resident also for tax-filing purposes, which will allow you to continue to file a joint return. If you make this election, Form 8843 is not required (because she will be filing her income with yours on Form 1040, not Form 1040NR).
This IRS website provides additional information: Nonresident Spouse | Internal Revenue Service. Remember: this applies for 2022. In 2021, you can file your return as you did in 2019 and 2020, and you may e-file the return.
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