I'm wanting to DM a comprehensive story throughout all the modules, in which a player can reuse their already created hero or make a new character with lore established throughout the adventures we've already done. My question is:
What is the chronological order of the modules so I can have my players do the stories in a way that makes sense.

Does the Horde of the Dragon Queen come before Out of the Abyss, or does the Dragon Heist come after Tomb of Annihilation?

There is an order, I don’t remember exactly what it is but the publication dates of the modules will tell you as they are all set in the FRs and it has an ongoing timeline that their publications are tied to.

Surprisingly if you look them up on Amazon it will tell you the month and year released giving you the order.

The modules don't have any set order. To my knowledge, they're all set roughly in the early 1490's DR, if you're running them in Forgotten Realms.

The only exceptions to this (to my knowledge) are Dragon Heist and Dungeon of the Mad Mage. DotMM is the sequel to DH, but they're so loosely connected that it doesn't really matter story-wise.

Publication date has no bearing on the chronology of the modules. Run them is whatever order works best for your group/party.

I'd recommend looking at the levels each module is for. For example, Lost Mine of Phandelver is for levels 1-5, meaning characters start at 1st level, then end at about 5th. Dungeon of the Mad Mage is for levels 5-20, so you could run LMoP then transition to DotMM, for instance.

Ok, once again, the Forgotten Realms has an actual ongoing timeline that proceeds at a regular rate against our calendar ( I believe it is roughly 1 month of FR time for every 2 months our time but that is off the top of my head not fact checked so it could be way off). Because of that the release dates of FR material actually tie into the FR calendar so a module released in may starts earlier in the FR year than a module released in October. Now given that several of the adventures tend over fairly long, in game, times it’s possible for things to overlap. The other problem is that several of the story lines are not just adventures but really campaigns that take the PCs from L1 to L13-15+ it may be hard or impossible to run them sequentially with the same PCs. The Phandalin modules available here on DDB are such that they pretty much can be run sequentially creating a fairly organized campaign. Lost mine + Dragon of Icespire Peak take you from L1 to L6, storm Lord’s Wrath and Sleeping Dragon wakes can take you to L10-11 and then Divine contention should take you to around L12-15. For my campaign I’m also mix;g in ghosts of salt marsh and some homebrew at the end possibly leading into a homebrew tier 4 campaign.

This link should help with the order and fitting the modules together into a campaign.

https://en.wikipedia.org/wiki/List_of_Forgotten_Realms_modules_and_sourcebooks

it should also help with finding stuff to get from DMsguild.

Taken from this page - https://alphastream.org/index.php/2020/04/09/the-official-timeline-for-the-forgotten-realms-and-its-adventures/

Out of the Abyss (1485 DR or later)
Hoard of the Dragon Queen and Rise of Tiamat (1489 DR)
Storm King’s Thunder (1490 or 1491 DR)
Lost Mine of Phandelver (Starter Set) (1491 DR)
Princes of the Apocalypse (1491 DR)
Curse of Strahd (1491 DR)
Tomb of Annihilation (1490 or 1491 DR)
Waterdeep: Dragon Heist and Waterdeep: Dungeon of the Mad Mage (1492 DR)
Dragon of Icespire Peak (Essentials Kit) (1492 DR)
Candlekeep Mysteries (1492 DR)
Icewind Dale: Rime of the Frostmaiden (Winter 1489 DR or later, likely 1492 DR)
Descent Into Avernus (1494 DR)
Acquisitions Incorporated (1496 DR)

The Wild Beyond the Witchlight (Date unknown, presumably after Rise of Tiamat)

Obviously not 100% up to date but it's a good foundation.