Assuming a fair shuffle we cannot assume a deck is uniformly shuffled. Thus is the nature of a fair shuffle. Uniformly means and implies either or both that things will be the same in all cases at all time, or occur in equal amounts, evenly.
A fairly shuffled deck of cards has 52! number of combinations. Millions of those combinations will be 13 cards of the same suit in a row. What has come before in terms of cards you know to have pulled influence the probability of what is likely to occur, but has no baring on what the next card actually it. We can say with a greater degree of certainty that it is less likely to be a card of the same suit, but there is still chance of it bucking the trend. You can only make calculations on what information you have, you can make assumptions but they are just that, assumptions. Your assumptions have no baring on what will come next, but can and should be used to make correct decisions based on maths.
I think comparing a shuffled deck game that has multiple stages of play to roulette may not be the best example. Roulette is easy to identify that the independent event was the spin and putting the ball in. However in a card game you could think that the independent event is each street, and they are in a way, but in terms of the deck, the independent event is the shuffle. Assuming a fair game again, even if you don't make it to see all 5 community cards, the deck has been set from the beginning of the hand, even if we don't get to see those cards.
Anyway to answer the main question:
But can we use the fact that a uniformly shuffled deck is unlikely to
have long streaks of one suit to estimate a lower probability?
Again we can't assume uniformity in a fairly shuffled deck, but yes what information we know influences the probability, which can be used to make decisions, however it does not change the reality of how the deck has been dealt.