If you really want get rid of flicker use for webcam a DC light source like those light strips
https://de.aliexpress.com/item/CRI-90Ra-5-mt-DC24V-SMD3528-Konstante-Strom-LED-Streifen-Licht-228-LEDs-m-mit-Konstantstrom/32671001877.html
https://de.aliexpress.com/item/5m-reel-DC22-27V-300-leds-2835SMD-High-CRI-90Ra-Constant-Current-IP20-non-Waterproof-LED/32544701096.html
https://de.aliexpress.com/item/TOP-bright-7200lumen-reel-Flexible-Led-Strip-3528-180leds-m-Double-row-10mm-width-FPC-DC12V/32656033340.html