Given that this bug has not yet affected a sufficiently large user base, Google does not yet have to acknowledge the issue or even issue a fix. While some users have claimed that a recent beta version of Google Messages seems to have fixed the issue (via 9to5Google), it is still unknown if this is really the case. In addition, the behavior of the problem is unpredictable, with some users claiming that they are not able to recreate the problem in all cases.
Since Google has not yet released an official update, users have suggested a few hacks as a solution to this issue. The easiest way to resolve this is by simply closing Google Messages from the “Recent” menu, after which the app should no longer have access to the camera. The second, more drastic option is to revoke camera permissions from the Messages app. However, this solution also means that you will not be able to use the live view feature in Google Messages until the permission is turned on again. While the method of removing camera permissions differs from one device to another, you should be able to hold the “Messages” icon and open the dedicated settings menu for the app on most phones. Once you have done that, scroll down to the “Permissions” section and then make sure that the part that says “Camera” has its switch set to “Do not allow”.