I think there are several interpretations, with no definitive rules support one way or another, so it's dm judgement call.
No, flaming sphere stays lit, and pyrotechnics causes the fireworks or smoke
The flaming sphere stays lit and you get the fireworks/smoke.
The reason the sphere stays lit is that it is fueled by magic, not mundane fuel.
While there isn't explicit rules support for this interpretation, it isn't unbalanced because it isn't more powerful than the spells separately, and deciding in favor of the PCs and the rule of cool argue in favor of it.
Perhaps for fluff it goes out during the fireworks/smoke, then relights.
A Contrary Argument
A contrary argument would be that you get either spell, but not both. Basically either one spell or the other wins.
If pyrotechnics wins, then the flaming sphere is extinguished and you get your choice of the fireworks or smoke.
If flaming sphere wins, then pyrotechnics fails to extinguish the flame.
This is making the assumption that the fire in the flaming sphere is magically fueled for the duration, and it seems reasonable to assume that it can't be snuffed the same way as a regular fire, because magic.
So how to decide which spell wins? Assuming they're both cast by the same caster, it seems reasonable to let the caster choose. If cast by different casters in an antagonistic situation, if the spells have been cast at different levels, higher level wins; otherwise, its a contest between spellcasting abilities.
No matter what, the fires created by the flaming sphere are fair game
You can use the flaming sphere to ignite something, and then use pyrotechnics to blow that stuff up like a boss, or, create smoke, of course.
Again, there's not much in the way of rules support, but if you think allowing the sphere to stay lit is overpowered, then perhaps this is the way to go.
Note:
My original answer was significantly different from this but editing it made me re-think it.
Both require you to be submersed in water to work. Now, if you were to fill the Bag of Holding with water first ... I'd say the Manta Ray cloak still doesn't work infinitely, because there's only so much oxygen in the water you can breathe.
The Cap however creates a bubble of air around your head, and doesn't insinuate in any way that the oxygen is taken from the surrounding water.
Best Answer
Theoretically Yes, but only works for negative con mod
Though it doesn't explicitly state it I would consider "engulfed by water" to be equivalent to being underwater. Thus triggering the suffocating rules.
However for most creatures the duration of watery sphere won't be enough to cause them to drown, even if they fail every saving through. Due to the duration of the spell.
Constitution below 10
Even for a creature with a negative constitution they would have to fail a minimum of 6 consecutive rolls before drowning. Assuming they have the worst stats in the world they will still succeed at least 30% of the time. (Probability of a Natural 20 from 6 attempts). Technically a natural 20 is not an auto-success on saving-throws but most tables I have played at accept it as a house-rule. So if you have a high saved DC (>20) or the target has a negative modifier in strength you may have a chance to succeed.
Constitution of 10 or above
Any creature with a constitution of 10 or above will never suffocate as they can hold their breath for longer than the spells duration. Though forcing them to hold their breathe can prevent them from casting spells or communicating which is fun.
Interaction with Hold Person
You mention that the combination of Hold Person and watery sphere could be quite strong. This would come from the effect of hold person.
The paralysed condition states
This would mean casting Watery Sphere on a target already held by Hold Person would automatically succeed. The extra save does increase your chances of the target reaching 7 rounds without saving. However, the chance of a creature having negative modifiers for Strength, Constitution and Wisdom is extremely low and it is likely that they will easily succeed at least one of these saves.