Blindsight is pushing it but still OK
According to Detect Balance, normal Dragonborn are worth only 21 points, one of the weakest races, vs. an average of 25 points. Darkvision is worth 3 points, so it would be not at all unbalancing to give darkvision to dragonborn, they would be average with it. (This is likely what I would do).
Value of Limited Blindsight. Blindsight 30 feet is worth 8 points, like an ASI +2 that can covert to any feat. 5 feet of Blindsight or the "Fighting Initiate" feat that grants 10 feet of Blindsight should therefore be worth less than 8 points. I think it better than "Blindsight 30 feet, blind beyond" when it comes to ranged attacks and spells, detecting ambushes and so on, and that ability is worth 4 points. So Blindsight 5 or 10 feet might be worth around 6 points.
That would bring you to 27 points, stronger than average but still in the recommended range of 24 to 27, and not unbalanced.
In my experience, blindsight even out only to 10 feet is quite useful. It allows you to detect scrying sensors, fight invisible attackers of which there are quite a few (e.g. duergar, oni, invisible stalkers, mages, imps, genies, pixies, slaadi and various other demons to name just a few ...), and fight in magical darkness or fog without disadvantage, which can be a brutal tactic if one of the party members can cast darkness or fog cloud.
Impact of Low-Light Vision. Your Low-Light Vision is a lot weaker than darkvision. The main value of darkvision is from being able to see in the dark, like in a dark dungeon, not from seeing in dim light as if it were bright. I would at best value Low-Light Vision with one point. This would lower the point value for many other character classes as darkvision is a common racial trait by 2-3 points. About half of the listed classes have it, lowering the average value to somewhere around 23-24 points. The loss of superior darkvision in comparison has no big impact, only very few classes have it and it is valued only one point above normal darkvision.
In such an environment, giving darkvision to dragonborn is still entirely within range, but giving Blindsight would push them just above the recommended range. There are still races that have higher point values though, for example variant human with 33 (which also is unaffected as it has no darkvision), so it it not entirely unbalanced.
Conclusion: You are right that how good it is on a character will depend on how much ranged attacking in dark environments they will do vs melee, and these kinds of dependencies are not well captured by the point system of Detect Balance. If dragonborn had Blindsight, I would probably not use a dragonborn for a sharpshooter build; but on melee fighters it would be strong. To avoid abuse and broken builds, it is wise to think about the build that would abuse it first, not about the build where it would be underwhelming. Therefore, I'd recommend to just go with darkvision as the enhancement.