From the intro in a Wired article,
Soviet Union built hundreds of sanatoriums across its vast empire for the relaxation and recuperation of its citizens. Such sanatoriums—half hospital, half spa—were ordained by Lenin himself, who in 1920 issued a decree entitled "On Utilizing the Crimea For the Medical Treatment of Working People." The Labor Code of 1922 declared that all working people must stay at a sanatorium for at least two weeks a year; at their peak capacity, in 1990, Soviet sanatoriums could handle up to half a million guests at a time.
(article also links to several interesting pics of the sanatoriums)
I'm thinking that at peak season the sanatoriums must be very crowded. What was a day in such peak season like? How large and jampacked one sanatorium could be in such season? Could people get enough rest during such time?
I cannot write a properly sourced answer without doing additional research into this specific topic, but what I want to communicate in very broad strokes is that the article oversimplifies things a great deal — especially considering that Soviet health resorts themselves, as architectural objects, are so widely known, depicted, and talked about today.
To get this out of the way right away: sanatorium / health resort vacations weren't mandatory. People were not expected to always spend their vacations there, nor were they forced to partake in any other organized vacationing. At most, you could call it peer pressure if a group from one's job went, or your number in line came up (see below).
The 1922 decree, as you may guess, was not a way to forcibly coerce people to stay at resorts, but an idealized milestone to strive for. In fact, the decree itself says nothing about a two-week vacation or that workers must (or rather should) be necessarily be able to visit sanatoriums: it just orders the necessary efforts for establishing this system of workers' resorts in Crimea using existing infrastructure (link includes a scan). If anything, even with all existing Pre-Revolutionary spas, resorts, mansions, and hotels in Crimea repurposed for this aim, the peninsula wasn't quite big enough to host the entire Soviet Union's workforce every year. (You also mixed up the "half a million" figure in the title: it was all of the thousands of sanatoriums in USSR, not just one. The USSR's population post-war ranged from 170 to 290 million).
The two-week vacation itself was mandated by labor rights, similar to the 8-hour workday. That right was indeed quite stringently protected — like in many other government-regulated areas, there was a lot of stability and safe predictability (if not always quality) in basic arrangements of one's life the Soviet Union: living space, job security, pensions, healthcare and so on.
Health resorts, which sanatoriums were, were simply an option that you could exercise through some official organizations. You needed to obtain a ticket, based on quotas, priorities, and queues stemming from quotas. They indeed were officially healthcare facilities, and tried to enforce a daily regimen, wholesome (if bland) diet, and various invigorating or therapeutic procedures on their guests; the guests generally accepted this pampering and dutifully underwent the therapy, but had leeway in how serious they took the "medical" side of the vacation. In any case, it was a very regimented affair, more akin to a preventative hospital stay, so "jam-packed" sanatoriums were not.
Now, how would a worker get an organized vacation, like a trip to sanatorium or a regular workers' resort (дом отдыха, "recuperation house")? Again, in broad strokes: you came to work, the word got around that spots in a (say, N Health Resort) are open for applications, you applied. Maybe you fit the quota right away, or you had to wait in line for some (long) time. The tickets/quotas could be from your union (this was where sanatorium vacations were distributed), or your company/factory, or some other org.
Some resorts were patronized (and even built) by specific large organizations, so you needed to be in the corporation to get a ticket. Others were for general worker population, depending on how the unions distributed them (so it could of course depend on some social capital, nepotism, favors, just luck). There were exclusive resorts built by and reserved for large orgs like major industrial firms or ministries, but also just regular ones for regular laborers.
It might be simpler to visualize a sanatorium if we also mention pioneer summer camps. Basically, it's a boy/girl scout camp, there are tickets that are available form your school or your factory or social services etc. etc. (see above), you work out dates during the summer recess, get your son/daughter on a train, forget about them for several weeks =) Point is, the opportunity is presented to you through your social circle or local announcement, and it has grounds that you're not supposed to leave, unless on a field trip or sneaking out. Oh, and just in case: not all (to put it mildly) summer camps, resorts, or sanatoriums were in Crimea, or sea-side.
Still, going back to the gist of my answer, many, if not most Soviet people simply spent vacations as people do. They sat at home watching TV or reading or making hobby crafts, tinkered with their prized automobile, went for a country or mountain hike with friends or with a tourist club, spent time in their hobby club, flew to another city to visit relatives, or went on a alcohol bender with friends or alone...
Specifically Soviet options were to go to their dacha (a small country house with a garden), or to a village where they had a house / relatives or friends with a house, and spend their vacation walking, swimming, picking berries and mushrooms, and doing country stuff around the house like splitting wood and gardening. Some were also avid hunters, who went on hunting trips (shotguns mostly though, apart from higher management, forest rangers, prospectors, and the military; rifles weren't sold in sporting stores during post-war Soviet era, you had to have access to them otherwise).
EDIT: I've expanded my answer and provided some sources below, in this comment.