Very quick and rough number crunching, based on the numbers given above and taking no modifiers into account, the net output of each agriculture district is trading -6 food, -2 minerals for +2.75 CG, +4 Trade Value. I wouldn't call it horrific, but seems pretty bleh to me. Before this thread I thought the civic was just replacing farmers with anglers, so you'd still 2 per district plus the pearl diver. Would be a lot better if that was the case IMO. A shame, I kinda like agriculture-focused builds like Agrarian Idyll, was looking forward to trying anglers.
Why are you calculating per district rather than per pop, or per units of CG produced? Pops are far more of a limiting factor than districts in the early game, and how efficient you are at using them is far more important than the total output of districts, which are only as limited as minerals are a limiting factor. You're also not factoring in how this rebalances the homeworld economy overall regarding your need for very expensive, mineral-hungry industrial districts right at the start of the game.
One of the biggest impacts of the Angler Civic is that it highly incentivizes NOT building tons of industrial districts on your capital, but rather to use your homeworld as an early farm/trade-energy world while you set up your guaranteed worlds as one mining world and one industrial world.
This is antithetical for most builds because you really want your worker economy to be getting 25% colony designations, but passable in the early game for Anglers because base 8 food per angler is
already a 25% food output upgrade for other empires, and the 4 trade value on your capital per 2 farm district workers basically covers your early energy worker needs as well.
Better, compare what it takes to produce 6 CG.
On the pearl diver build, it takes 2 pearl divers (2 pops) to produce 6 CG. They are also producing 4 trade, which is 4 energy. This takes 2 farm districts (2x 250minerals), 4 minerals in upkeep (2 per angler).
On a normal empire homeworld, 6 CG takes 1 industrial district (1x 500 minerals), 6 minerals a month in upkeep.
On a net the 'normal' empire saves 1 pop directly employed for the 6 CG, but loses out on 2 minerals a month and 4 energy. That's basically another homeworld pop in and of itself, washing out the pop advantage,
and if you were relying on the homeworld for raw materials these are two jobs that DON'T get world designation bonuses.
(And this is without factoring in the Anglers, with their 2 extra food and 2 extra trade.)
There's multiple implications for these- that you don't need a designated farmworld as one of your first three colonies, that you'll be able to afford the food and CG of a colony ship much easier than other empires letting you start colonizing planets faster if you have the alloys, that you'll need far fewer miners because each district is cheaper than going for the Industrial districts- but one of the more important implications is that this lets you use one of your guaranteed colonies- the one not immediately made into a mineral-colony- as your alloy economy to make up the alloy dynamics not addressed above.
If you put up your second colony as an alloy world, you can make use of the alloy-world designation you can't use on your homeworld. This will give you a 20% savings on mineral upkeep used to produce each set of alloys- about 2 minerals an industrial district. If we just stopped your back-of-the-napkin math here, it should already be calculus changing: for the same number of farm and industrial districts you could add +2 minerals per Industrial district to the Angler side, as long as you move your industrial worlds off-homeworld.
But even this can be taken further with potential combos. If you take Aquatic, your guaranteed worlds will be 100% habitability, meaning no alloy production inefficiency on the colonies, even as you'll get more value from your homeworld's early resource production. If you take Catalytic Converters as a second civic, you'll be able to use those major food stockpiles to maximize war potential beyond what a mineral economy could support. If you're a trade built, you'll be getting far more value out of your trade-trait much earlier than you could from clerks. If you're a tech-build, you'll be able to afford more homeworld scientists significantly sooner by avoiding the pain of expanding alloy production with homeworld industrial districts. If you've a bunch of colonies to colonize, you'll be able to ramp up food and CG production for colony ships far faster and cheaper than alloy-CG. If you're an Authoritarian build, you can get worker and slave bonuses to your CG bonuses, without having to pay higher CG living standards for CG production, thus giving you more CG for more specialists. Etc. etc. etc.
Like Catalytic Converters, Pearl Divers is an economy-re-arranging civic. It's not just a 1-for-1 swap comparison, but what those swaps mean as macro-economic rebalances occur.