I deleted all the Square WebPay files via WinSCP and reinstalled the module. Still no joy. I did get a warning log:

File Contents( /home/vinyld6/logs/myDEBUG-adm-20220515-180033-869325-warning.log)
[15-May-2022 13:00:34 America/Chicago] Request URI: /VDSstore/***/index.php?cmd=modules&set=payment&action=install, IP address: 152.97.210.26
#1 square_webPay->__construct() called at [/***/modules.php:106]
#2 require(/***/modules.php) called at [/***/index.php:11]
--> PHP Warning: Use of undefined constant MODULE_PAYMENT_SQ_WEBPAY_TESTING_MODE - assumed 'MODULE_PAYMENT_SQ_WEBPAY_TESTING_MODE' (this will throw an Error in a future version of PHP) in /includes/modules/payment/square_webPay.php on line 106.

[15-May-2022 13:00:34 America/Chicago] Request URI: /VDSstore/***/index.php?cmd=modules&set=payment&action=install, IP address: 152.97.210.26
#1 square_webPay->__construct() called at [/***/modules.php:106]
#2 require(/***/modules.php) called at [/***/index.php:11]
--> PHP Warning: Use of undefined constant MODULE_PAYMENT_SQ_WEBPAY_ACCESS_TOKEN - assumed 'MODULE_PAYMENT_SQ_WEBPAY_ACCESS_TOKEN' (this will throw an Error in a future version of PHP) in /includes/modules/payment/square_webPay.php on line 111.

Does this log help ID the "Whoops!"?

My next step will be to restore my site.