So we can all browse the folio to see what things are available to craft at higher proficiency, but there are also a lot of hidden information out there, especially for the professions that don't craft anything. It would be helpful for everyone to have a discussion here and combine out knowledge. Below is everything I know, gained by intensively reading the folio and wikis as I waited for airships and carriages.

For every profession, there is a labor cost and craft time reduction of 5% for every rank increase starting at veteran (except for Authority to Champion where it is 3%). The max proficiency is 90k.

There are 21 professions in this game. By default, you can level each up to 10k proficiency, but only 7 of these can be upgraded into the next tier (Novice: 10k-20k). Six of these can then be upgraded in the Veteran tier (20k-30k), and so on. Authority is 50-70k, and Master is 70-90k. You can only Master 2 professions.

You can buy Specialization Snowflakes for 200g each to increase your limit at every tier by 1, meaning that with 1 Snowflake you could Master 3 professions. Each character can use a maximum of 13 Snowflakes.

Fairly straightforward. You can craft more stuff at higher levels. The highest I can see is the Ancient Library Relic which requires 60k proficiency.

A "for fun" profession that doesn't seem to impact the gameplay. You can compose musical scores and then play them back on various instruments. The composition requires actual real world skills. Nothing here has a proficiency requirement to craft, but a higher level means you can compose and play longer, more intricate pieces of music. Trying to play a piece of music above your level will cause you to make random mistakes. The value here will depend on how whimsical people on your server are: I can just imagine the theme to Pirates of the Caribbean playing as a band of pirates come to steal your stuff, or the Rains of Castamere during a siege.

Make wooden weapons and furniture. The only furniture that has a proficiency requirement are the beds which restore labor every 22 hours. The highest level bed requires 20k proficiency. The top tier weapons require 50k proficiency.

You gain construction by building houses and probably castles and defensive fortifications. Construction time decreases with level, which might be helpful to avoid getting ganked as you build in pvp zones like Auroria. At 5k you can build the Gazebo Farm which is the upgrade to the Scarecrow Farm. Honestly, there doesn't seem to be a reason to take this past 10k.

The profession for making and turning trade packs. By default, making and turning in packs cost 60 labor each, so any labor savings is worthwhile. Also, a higher proficiency increases the chance of a negotiation bonus, but it is rare. Supposedly it's only about 5% of the sell price. The highest requirement is the Bird's Eye Telescope at 10k.

Craft food that restores health or mana or gives temporary buffs. Highest are the feast tables which require 60k.

Craft various accessories and musical instruments. You can also make fishing rods and beehives for other professions. Highest are the various accessories at 50k.

Better chances at rare drops and quantity when doing husbandry actions. Can make animal pens to increase husbandry efficiency at higher levels. Highest is the Blizzard Bear Pen at 60k.

Better chances at rare drops and quantity when doing farming actions. Can make seed bundles to increase farming efficiency and output at higher levels. Highest is various bundles at 45k.

Better ability to catch valuable fish when sports fishing. Higher proficiency means you can do more damage to rare fish quickly. These fish become trade packs that you can turn in for a lot of gold.

Exactly like Farming, but with herbs and flowers instead.

You get larceny by opening coinpurses and by uprooting plants. A higher larceny proficiency decreases the chance of leaving evidence when committing crimes. It also is supposed to increase the yield and chance for rare loot from opening coinpurses.

Same as Metalworking and tailoring. Make leather and leather armor. You obtain leather by slaughtering turkeys, pigs, etc. You can also make nets to catch world bosses as battle pets and to catch queen bees for beekeeping. Highest requirement is 50k for top tier armor and mass production of leather.

Better yield and chance at rare drops. Can make woodlots which save space and labor to harvest. Highest is the Pine Woodlot at 60k.

You can make submarine parts at 25k. You equip these on a submarine to give it various abilities. Machining is mainly for reforging all crafted items, combining 3 items of the same level in order to reroll its type. Reforging requirements cap at 25k, but it is so labor intensive that leveling Machining beyond that for labor reduction makes a lot of sense.

Make stones bricks for other professions and for buildings. Also makes hereafter stones which will always be in demand. The labor savings could be worth it. I admit that I don't understand the deal with the 3 Runes and the Fortuna Die. It looks like you use 2 Runes to create a buff, and you can enhance the buff with the Die. Good for PvP and PvE, I guess. Highest requirement is 50k for mass production of stone bricks.

Smelt metals and make plate armor. Highest requirement is 50k for the top tier armor and for mass producing iron ingots.

Increases yield and chance of Fortuna Veins showing up. A higher level supposedly increases the chance of finding gems, but I've heard complaint that people don't notice the difference. Either way, the labor saving could be worth it. Vein in Auroria will require 50k proficiency to mine.

Mainly for making regrade scrolls which don't require a minimum level, but if you make a lot of them the labor savings would be worth it. Also, you can make The Art of Language to learn other language in the game, letting you listen in on what the opposing faction is saying. Highest requirement is 50k for the two spellbooks which give 30 minute buffs. Notably, these spellbooks are relatively easy to make.

Same as Metalworking. Make fabric and cloth armor. You obtain fabric by growing cotton or shearing sheep. Highest requirement is 50k for top tier armor and mass production of fabric.

Make metal weapons and shields. Also makes ammo for ship's cannons and harpoon guns. Highest requirement is 50k for top tier weapons.