Hi neighbors! Is there anything showing that the transformer itself is no longer powering, or is it the Video Doorbell Pro that is just showing offline? The Transformer should still be outputting voltage, and the Doorbell Pro will only draw power at a rate that should not exceed a new transformer.
As you mentioned having a multimeter, a great step will be to check the transformer after the Pro goes offline to decipher whether the transformer stopped powering, or if the Pro stopped receiving power. When wiring directly to a transformer, using the Pro Power Kit in bypass mode is the best step. As I see you’ve covered this step, the Doorbell Pro should be working as intended.
Please ensure there is not any resistance in power, which can be caused by thin wiring, old wiring, a very long wire run, or a short in exposed wiring. Once your Ring Pro is setup in the Ring app, it is important to also select No Chime from the Doorbell Pro’s settings in the Ring app. If this does not resolve your concern, feel free to include pictures of wiring at the transformer and behind the Pro, for a closer look.