You said it yourself: the shield is weak. It doesn't matter if the lingering effect(which is NOT an aura) has 3 seconds to tag people, between the shitty effect and the nonexistent duration, it's illogical and counter-intuitive to do so as you lose dps for running around and worse, you risk mispositioning yourself. She's the squishiest character in league, if you get within 400 units of your front line to apply a half-second shield that couldn't block a minion auto, you're asking to get disintegrated by a single AoE spell.
I don't feel like I hit lvl 16 much when I play support with sona (or supports in general), so I do think it is a bit silly for a support to be level reliant, although the way you phrased it implies that her basic abilities have been nerfed to load cd into her ult.
Is this the case? Am I understanding you properly?
You are understanding her correctly. When the initial 4.13 rework happened, Rito intentionally severed the numbers on all of her spells, both their primary actives and replaced her auras with shit secondary lingering actives, so they could intentionally trap additional base numbers into R ranks. Supports are meant to be at their strongest during laning phase, but Rito intentionally gutting Sona's lane potential for late-game power is an inherently flawed concept that should've never made it onto paper, let alone onto Live. Then in 6.14, removed more strength from her basic abilities and traded out the bonus bases on R ranks for artificial CDR instead, which cause an additional problem: although this gave Sona SLIGHTLY more dps and Healing/ps, it was at the cost of higher mana expenditure, for having to spam spells to get the same result. As the enchanter with the lowest base mana in the game and the most expensive heals, this is another flawed design that pushed Sona even farther into the unhealthy. This also created this illusion where people thought Sona was "OP" for half a week, when she was still matter-of-factly WEAKER than pre-4.13. I looked at the numbers, her dps, healing and everything were still lower, but people weren't given enough time to realize the original 6.14 numbers were still bad, because Meddler came in after only 2 days to jump on the opportunity of excused Sona guttings before the fallacy could dissipate from the community's minds.
The short uptime of shield is a big problem, but I think its that way because you can apply it...repeatedly quickly.
Except this was not the case when the spell was first implemented. She didn't receive artificial CDR until 6.14, but the 1.5-second duration is a hold over from 4.13. The shield and 6.14 are unrelated, it's that way because Rito intended to dumpster Sona.
Sona's numbers are surprisingly high, but I don't think it feels like that because of the cds.
This is just a blatant lie. Look at the numbers yourself, the dps, the shielding/ps, the healing/ps, all of these are lower than the rest of the support cast. Even after taking artificial CDR into consideration, her numbers are still embarrassing.
The fantasy of a "late game support" is impossible to achieve, these two concepts are in direct contradiction of each other and if you were to create such a monstrosity that's powerful both in lane and end-game, you'd probably end up with something with infinite scaling that looks a lot like this:

The idea of spell-spamming on the most mana-gated enchanter in the game, is inherently flawed. I shouldn't even have to explain this.
The fallacy of Sona being a "backline non--interactive aurabot" or something of the sort has never been true in the history of this game. This is a lie propagandized by players that have never played Sona before, which is only bought into by sheeple who likewise have never played Sona before. Ask any pro player or any experienced Sona player and they will tell you Sona has always been aggressive support and the intentional misconception of Sona sitting back is nonexistent in literally anything above bronze. It never existed and Rito abused this lie to intentionally dumpster her.