Welcome to allnurses!
A BSN-completion program is certainly a possibility, but keep in mind that it will not cover anything about clinical skills -- the curriculum will not repeat any of the content from an ADN program, only the additional material that makes the difference between an ADN and a BSN (typically, management/leadership, research, and community/public health, plus the general ed requirements to complete any
BS degree). So, it will not address the concerns that recruiters and potential employers have about you -- your limited/dated basic clinical skills and knowledge. Also, BSN-completion graduates are not considered "new grads" since you have to be a licensed RN to get into a program, so it wouldn't get you a "do-over" as a new grad.
Unfortunately, this is a v. difficult time for anyone
to be looking for a nursing job ... IMHO, a refresher course would be your best bet in terms of finding employment. However, completing a BSN would certainly expand your career opportunities over time. Best wishes!