Is it possible to save voicemails when I only have an older Republic phone that is no longer receiving software updates?
Voicemails are saved in the network carriers side until you delete them (even though it may not look like it). If you were planning on getting a new phone all the voicemails will show up after you call once with your voicemail password. If you are very concerned about it and it has a new enough version of the dialer, you can click the voicemails and share the ones you want to keep and send them to your email.
Note that this is not true about SMS messages or call history, make sure to back those up before switching (there are several apps, find one with good reviews and make a backup off of the phone (google drive or maybe nextcloud if you don’t mind a harder setup).
If you’re referring to this process: How to Save a Voicemail Message – Republic Help it is available only for our 3.0 phones.
Anything that can be listened to can be recorded.