Thanks, you had it correct I think.
I restarted the tutorial, slowed the speed down and was much more deliberate about everything. When I went to war with the Samnites I paused frequently to examine armies and inspect all of the action. A lot of armies that flooded in were my subjects sending troops and also enemy troops from a Samnite alliance. I have a much better understanding of the war and how I would approach future engagements.
I also learned a great deal more generally about the game since I have been pouring over the menu screens. I completed 10 of the 13 tutorial objectives and am now deciding if I want to continue the tutorial (basically playing out a conquest-heavy game as Rome) or start a new game with a different power.
Prior to declaring war on the Samnites I was closely watching the Senate approval of a war declaration. Most of the time the in-favor votes hovered around 48/100. I held off declaring war and let some time pass and also changed my diplomatic stance and was able to get Senate approval up to around 57/100 for a war declaration, but a Declaration would still incur a 5 point corruption(?) penalty.
Is there a way to increase Senate seats approval of something like a declaration of war? Do you need to interact with the factions, leaders of factions, or some other method? Or is it a moot point and not something to fuss with?
Funnily enough, the current makeup of the Senate seems quite happy to wage war with anyone NOW as most nations I check I have over 85 seats in favor of war declarations after I won the war with the Samnites.