Ring Video Doorbell Wired + Pre-existing Doorbell >> into old transformer

Hello. First post here. I am installing a Ring Video Doorbell Wired at my parents house for their peace of mind. I have replaced the doorbell button on the front door no problem. They have an old house with an existing doorbell system linked to a mechanical bell, which I would like to keep. The Ring doorbell activates/boots, but then keeps rebooting every ten seconds or so. When it is stable, then I can get the app to recognise it, but it does not turn white and will not stop flashing blue when I want to connect it. I think the issue is the transformer. Do I need to use the bypass cable? The transformer box is old and janky. Any ideas as to what to do with it? Would greatly appreciate any help or guidance.