Can this 2023 version of Turbo Tax also be used in 2024?

No.  You have to buy a new program each year or use the Online version.  The Online version is only good for the current year.  

You can buy the Desktop Download program here or in stores or online like Amazon, Costco, etc.
https://turbotax.intuit.com/personal-taxes/cd-download

Authorized Sellers
https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-product-orders/obtain-authentic-turbotax-programs/L1yYfitCw_US_en_US?uid=lv4rnzmq

2024 Turbo Tax Desktop Download System Requirements
Windows 10 or later or Mac OS Ventura 13 or later (newer). 
https://turbotax.intuit.com/personal-taxes/cd-download/tta-system-requirements

The 2023 version of TurboTax cannot be used to file your 2024 taxes. Each tax year requires its own specific version of TurboTax software, which is updated to reflect the tax laws and forms for that year. 

• Purchase 2023 here
• Access 2024 here.
• Some versions of 2024 are free and can be completed online. 2023 is available for purchase and download.