Measured, not estimated
Every contrast finding carries the computed foreground and background, the measured ratio, and the threshold it was measured against — which depends on the text size and weight, not just the colours.
Try shades until one passes
A slider walks the foreground colour lighter or darker, showing the ratio live and marking the first shade that passes. The suggestion is the nearest passing colour rather than an arbitrary one, so the change to your palette is as small as it can be.
The result is a hex value you can paste.
Worth knowing: Contrast is measured against computed styles. Text over an image or a gradient has no single background colour, and those cases are reported for review rather than given a ratio that would be fiction.
Start with the page you are on
Install the extension, press F12 and open the Accessibility tab. No account, nothing to configure, and nothing leaves your machine.