It does appear to be a script related to your GA via GTM that may be butting heads with our embed snippet's built in behavior to pass the site search query value to your GA endpoint.
In the past I've seen asset load order being the culprit, so I did a quick test with a barebones HTML boilerplate and added your Swiftype embed script before the GTM script within the <head></head> container and then included the input element within the <body>.
Under these circumstances the search overlay performed as expected without triggering the error.
I'm afraid we're unable to support or debug non-Swiftype related scripts/conflicts, but if you're able to pinpoint a valid bug we can escalate to our engineering team.
I hope this helps!