Your speed will be 0 until the end of the turn
As quoted in the question, the description of the Steady Aim optional class feature for rogues says (TCoE, p. 52; emphasis mine):
As a bonus action, you give yourself advantage on your next attack roll on the current turn. You can use this bonus action only if you haven’t moved during this turn, and after you use the bonus action, your speed is 0 until the end of the current turn.
This statement is setting the speed to an absolute value, and it defines the timeframe to be until the end of the turn. This is independent of the underlying speed. A wood elf barbarian with a base speed of 45 feet would be set to 0 by this feature, just as a halfling cleric with a speed of 25 feet would.
From a narrative/flavor perspective, the name of the feat implies that you stay put to get a better aim on your target. Page 62 of Tasha's Cauldron of Everything displays a drow rogue kneeling down to take aim with a crossbow (just below the description of Steady Aim).
The College of Swords bard's Blade Flourish feature description says, in part (XGtE, p. 15):
Whenever you take the Attack action on your turn, your walking speed increases by 10 feet until the end of the turn, [...]
Blade Flourish increases your walking speed by 10 feet until the end of the turn, so if you had originally a walking speed of 30 feet, it now would be 40 feet. Then, due to the ongoing effect of Steady Aim, this speed is 0 feet.
D&D 5e has no formal stack which is used to apply and resolve effects in timing order.
Again, this also makes sense from a narrative perspective. Blade Flourish is intended to express "impressive displays of martial prowess and speed", the rogue doing somersaults and dashing about like in an Errol Flynn movie. This does not make sense with at the same time kneeling down and taking steady aim at someone.
To me it feels that other interpretations would be technical semantics to eke out a combat mechanical advantage from combining features against their spirit. Your DM may be down with that, and as in all adjudication cases, may give you pass to do so if you both have fun with it.
(There used to be guidance that you should consider combining any of the auxiliary works (Tasha's Cauldron of Everything, Xanathar's Guide to Everything, Volo's Guide to Monsters, etc.) with the core rules, but not several of them together, to avoid the otherwise unavoidable explosion of combinations that at some point will yield broken ones, but it is not official any more.)