I originally shut down my C-3 back in Feb since we were moving... I got it going again recently at our new house with some new devices and the logs are still there from back then and with all the old devices, of which I don't have...
Can I safely do a soft reset to clear the logs and restore the backup on a C-3
You can; a soft reset is generally safe, as long as you restore a backup you have and don't reset anything else. (The logs are not stored in this backup, and you'll get an option to clear them during the soft reset, so that will achieve that goal.)
However, there is also no reason to. Old/past logs will be purged automatically in accordance with the total-size-based limit, so your "old" entries will eventually age their way out. So, unless you have a reason you want to get rid of them right now, I'd probably just wait -- it will happen on its own, and there are tools to filter logs based on date (among many other options) if needed at any time.