If, after pausing, I choose actions for my characters, the actions go off, as expected.
Then, the regular initiative turn order starts and the first character of mine has none of their actions and can only end their turn. They should have a full round. The rest of the characters perform normally.
I think this is a balancing issue. If you get your "stealth action" out with all 4 characters AND get a surprise round, combat would be completely trivialized by stealth.
RAW 5e also suggests that the way Solasta (tries to) handle stealth at the start of combat is correct. At the table, your DM would adjudicate which action causes the combatants to roll initiative (basically the first aggressive act). Then, everyone who was unaware of a potential threat is counted as surprised for the first round of combat, but other than that actions are resolved in initiative order.
At least that's how I run my games. Six people yelling at me how they want to shoot their bows/spells at the shady merchant and his entourage of bodyguards in the middle of a conversation? You better believe I have them roll initiative before a single attack or save is rolled.
I do agree, however, that stealth is behaving weirdly at the start of combat sometimes. I've had situations where a character of mine didn't get their main action on turn 1 because I cast Hunter's Mark as my "stealth (bonus) action".
btw when I say "Stealth action" I mean the action(s) that trigger combat - the aforementioned "first aggressive act"
RAW 5e also suggests that the way Solasta (tries to) handle stealth at the start of combat is correct. At the table, your DM would adjudicate which action causes the combatants to roll initiative (basically the first aggressive act). Then, everyone who was unaware of a potential threat is counted as surprised for the first round of combat, but other than that actions are resolved in initiative order.
In RAW 5e if your party spots an enemy while remaining in stealth themselves, each character can use Ready action for an attack/cantrip/... before the combat starts. Then every party member shoots an arrow or something at the same time as their reaction, starting a combat and still having their actions, bonus actions, etc not spent and ready to be used on the surprise round. Though your GM might rule "turns out of combat" in a manner which won't allow it.