False, COVID vaccines do not inject any element capable of connecting with electronics through bluetooth.
The reason why COVID vaccines don't connect people through bluetooth is because if you look at the list of ingredients of the AstraZeneca vaccine, the list doesn't include a microchip or any ingredient that would cause the vaccine or vaccine recipient to have bluetooth connectivity.
I sent you the list of ingredients that the AstraZeneca vaccine has...
https://www.usatoday.com/story/news/factcheck/2021/05/27/astrazeneca-covid-19-vaccine-doesnt-enable-bluetooth/7452794002/
https://www.tga.gov.au/sites/default/files/cmi-approved-covid19-vaccine-az.pdf