Before the innovation of canned food and baked bread on ships, how did ocean-going vessels on longer voyages (exploration, trans-oceanic trade, or Naval Campaigns) manage to feed their crews to keep their health and strength up sufficiently for service?

Just to add another source to the expert response already provided, John Josselyn detailed his travels to North America in the mid 1600s including a detailed "meal plan" for any others planning to make the voyage. This is, of course, specific to those destination traveling by sea as opposed to navy men or pirates, but it gives a cool account of what a new colonist or traveller may expect (or an instructional how-to on feeding your group) on the voyage. I gave the following in response to a similar question, [How many supplies would you need to stock a ship in the Age of Sail?] (https://www.reddit.com/r/AskHistorians/comments/hm85os/how_many_supplies_would_you_need_to_stock_a_ship/).

The following is taken from An Account of Two Voyages to New-England, Made during the years 1638, 1663 authored by John Josselyn, Gentleman, and published in the 1670s with its companion, [New-England Rarities Discovered] (https://books.google.com/books/about/New_Englands_Rarities_Discovered.html?id=iWSC6HwiixsC&printsec=frontcover&source=kp_read_button), the first botanical and wildlife book on New England, which are both written in an older English. In addition to use of a medial s (which I have replaced with modern rules), he says things like "bear" instead of "beer" and "followeth" instead of "follows". I have translated most of this quote to modern English, keeping his neato archaic spellings but with (parenthesis) afterwards indicating a more modern translation as well as replacing confusing usage with my terms in [brackets]. Otherwise it is as it appears originally in his book.

The common proportion of Victuals for the Sea to a Mess, being four men, is as followeth (follows);

Two pieces of Beef, of three pound and 1/4 a piece

Four pound of Bread

One pint 1/2 of Peas

Four gallons of Bear (beer), with Mustard and Vinegar for three fresh days in the week

For four fish days, to each mess per day, two pieces of Codd or Haberdine (Atlantic Cod), making three pieces of [each] fish

One quarter of a pound of Butter

Four pound of Bread

Three quarters of a pound of Cheese

Bear (Beer) as before

Oatmeal per day, for 50 men, Gallon 1, and so proportionable for more or fewer

Thus you see the ships provision, is Beef or Porke (Pork), Fish, Butter, Cheese, Peas, Pottage (vegetable stew), Water-gruel (Oatmeal), Bisket (Biscuit), and six shilling Bear (Beer)

Summary - We see the meat portion above the clarity break is per 4 men for three days. Add to this the fish portion composing the other four days and you'll get weekly rations per 4. These supplies would not cost the same in London as the Bahamas, particularly butter, beef, and cheese (if you could find them in the 1680s Bahamas which I doubt) so that wanders from your question a bit. He goes on;

For private fresh provision, you may carry with you (in case you, or any of yours should be sick at sea) Conserves of Roles, Clove-Gilliflowers, Wormwood, Green Ginger, Burnt Wine, English Spirits, Prunes to stew, Raisons of the Sun, Currance, Sugar, Nutmeg, Mace, Cinnamon, Pepper and Ginger, White Bisket, or Spanish rusk, Eggs, Rice, juice of Lemmons well put up to cure, or prevent the Scurvy. Small Skillets, Pipkins, Porrengers, and small Frying Pans.

Ships didnt have cooks for passengers (they usually did for the crew), though a war or pirate ship would likely be different than a voyage ship like those taken by colonists. Here he is advising to each party to take these items for themselves as opposed to general provisions, if any were to be supplied. If not, he provided what those should be already, split by four people. This isn't a mandatory list and most pirates wouldn't have access nor desire to carry so much. But for a London traveller, it was a proper recommendation.

While he didnt list individual prices for the above, he did go on to list long term provisions - from hogheads of Beef required for a year to how many hats, shovels, or wheelbarrows to buy, what a family of 6 would need, how many copper kettles, muskets, swords, armor plates and pounds of powder & shot, which is all charted with British Lsd markings (L pound, s Shilling, d Pence). It may be viewed in its entirety [here] (https://books.google.com/books/about/An_Account_of_Two_Voyages_to_New_England.html?id=eIlDAQAAMAAJ&printsec=frontcover&source=kp_read_button) and in addition to the above mentioned contains detailed records of his travels to America.