how to know if this is real in regards to mouse

[Frenetixx]

hi there, 

 

I am looking for a wireless mouse that can connect to my phone, I want this because I want to use Samsung Dex on my chromebook, and when I connect with dex it loses the inputs on the chromebook and relies on the phone, and the phones track pad is really bad to use

 

I cant tell on amazon which mice can achieve this, I need something with bluetooth that does not require a usb dongle since im using phone. So I can tell which mice will work its confusing because most of the ads of a dongle and I cant differentiate them , im looking for something really cheap pls help thanks

 

would this work? https://www.amazon.ca/Bluetooth-Rechargeable-Wireless-Computer-Desktop/dp/B09PHKWCR4/ref=sr_1_1?crid=153QG1DIWH6VG&dib=eyJ2IjoiMSJ9.-MHjmeAW6ZlE4nBxvo-3QKlnAjNTetfewjzhQa0oJHGqOc5RlBxB8LiRsB2bPcbWsls_O6FgYKqoakLltkKdAk3prfz3svD8FnnJQLb7ys0Fs5_iM8clkljAcSZH15ZoMUGfR7WyQr64vb6u8zzsV_K_7c219rm0tki2ZR2Au_gV3NfJHvI9yotpbkoDkV-a2bSz9i41MSNHFjvSyRMa43nkcBXibS8-Hf9cjSq9DnIIEQ8wr-FCLlj7JlinDgZdsPCmOEhPvVqwfMDjzWqE1GdtATKT6C_gkdlJx1vZ714.ElW1LP1CSSnnGNx2RRW6jLYj9emH3Tgnrnkfcxa8AqY&dib_tag=se&keywords=bluetooth%2Bmouse%2Bfor%2Bphone&qid=1709689715&sprefix=bluetooth%2Bmouse%2Bfor%2Bphon%2Caps%2C190&sr=8-1-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1