I've had linearised plasmids stored for months at -20C and used them for cloning - no problems whatsoever. If you're unsure about your mRNA synthesis product you can run the product on a gel and see if you get a sharp band of the expected size. Or use Bioanalyzer chips if you have access.

For almost all purposes, your plasmid should be fine. I've used successfully used DNA samples that are much older. Be sure to avoid repeated freeze/thaw cycles, as this will shear the plasmid (make aliquots, if needed). I usually store DNA for short periods of a few weeks in TE at 4oC. The TE buffers the solution and chelates divalent cations (needed by nucleases). If you're worried about downstream effects of TE, store the DNA at a higher concentration and dilute when needed, or use "low TE" which is 10 mM Tris / 0.1 mM EDTA.

See also this ResearchGate thread:

https://www.researchgate.net/post/Best_long_term_storage_method_for_DNA

when DNA or RNA is clean it can be stored at -20C for many months without any degradation. and actually even at +4C. so you should be fine...

At -20C it should be fine even in water, assuming it is high quality pure water. However, if the enzyme(s) you used to linearize the plasmid left sticky ends (base-pair overhangs) you may have lost many of them so expect your ligation reactions with this DNA to be less efficient. Circularized plasmids can be stored in water at -20C for months on end. I elute and store my plasmids in irrigation quality (very pure and pyrogen free) water and my transfections with these plasmids are always very efficient. Good luck!