Audio Delay Test is a set of free browser tools with no signup: a sync slider, a tap test, a Mic Latency Test, a Bluetooth Delay Test, a Lip Sync Check and a Left/Right Sound Test. The page cites ITU-R BT.1359, with about 125 ms noticeable and 185 ms unacceptable. Only the Mic Latency Test uses the microphone, and only with your permission.
Find out how many milliseconds your sound lags. Line up a flash and a beep, run an automatic microphone loopback test, compare wired vs Bluetooth headphones, or check TV lip sync with a full-screen pattern. Free, no sign-up, runs in your browser.