Not much will change (probably)
1. Sieges. Battles were never a common activity in medieval warfare. They get featured in the popular imagination because they are spectacular events that can seize the imagination, whether they are being recounted by a grizzled old veteran or portrayed in a Hollywood special effects extravaganza. However, the reality is that siege warfare was the most common method of waging war. The attacking force can use a siege to avoid committing to action and a possible defeat, while the defending (outnumbered) side is forced to participate unless they are willing to surrender the castle / town / city without a fight. Sieges also allow far more opportunities for negotiated settlements and gracefully backing down from a losing position than the chaos of a battle. Given that the potion enhancements are not listed as protecting from starvation or dehydration, the presence on either side of soldiers with enhancements will have no effect on the outcome of a siege nor any influence on the choice of siege warfare as a tactic.
2. Economics. A two-year course of magic potions is likely to cost quite a lot. While the OP has not given any indication of how much it would cost, it is stated that this is a way of preparing soldiers, rather being a routine vaccination for every person in society. The problem here is that there were very few professional soldiers in this period. Levies of troops were pressed into service when required with a few days or weeks of notice (not two years!), then sent back to their farms after a conflict was over. After the Roman Empire collapsed, no European civilization was wealthy enough to support a standing army until hundreds of years after the Norman conquest. The nobility and their selected retainers were the only "regular" soldiers around, which means that they are the only ones likely to be potion-enhanced.
(Frame challenge - if you are a ruler with access to finite doses of immunity-to-bleeding-and-bacteria-and-fungi potion then the people you should give it to are not soldiers but reproductive-age women. Childbirth was a horribly risky business for women in that era, with many (most?) of the deaths of mothers resulting from bleeding or infection.
Increasing the survival rate of your nation's mothers will increase your working population / economic strength and therefore army strength far more than having a few tough soldiers.)
3. Battles. So let us examine what will happen when the potion-enhanced soldiers finally engage in battle. Do they throw away their armour and charge forward with two-handed swords screaming "There can be only one!" like the immortals in Highlander, seeking to decapitate their foes as the only way to win?
As forces close, arrows may start flying. For a soldier who cannot bleed out, these will probably not kill without a freakishly unlikely shot to the brain, but they can still cut muscles and tendons and (if really unlucky) pierce lungs. Grazing hits and bruises will no longer be a threat, but getting an arrow stuck into a soldier will make them combat ineffective until the arrow is removed without damaging more tissue and the cut tissue heals. (For those whose knowledge of archery is limited to Hollywood or modern target archery - a soldier who has a warbow arrow sticking out of them is not going to just snap it off with one hand and keep going. Warbow arrows were really solid chunks of wood to withstand the force of being shot from really powerful bows.) So soldiers will still want armour and shields to protect themselves while closing.
Once the troops get to melee range the same provisions that apply to arrows apply to spears, swords and other stabbing / slashing weapons - less danger of bleeding out from shallow cuts, but damage to muscles will still make a soldier combat ineffective. Bashing weapons will also have reduced effectiveness - bruising is no longer a threat (depending on how quickly the bleeding is stopped) but broken bones will disable a soldier.
In short, the same weapons will still be used in the same way with the same tactics. The big difference may be at the end of the battle rather than during it.
- Most soldiers on both sides will still be alive and uncrippled. Crushed lower spines will account for most of the cripples, crushed skulls or upper spines will account for most of the kills. (Decapitation or chopping clean through a limb was uncommon in battle.)
- Far more injured (enhanced) soldiers will be able to run away than would otherwise.
- Effect on overall fatality rates depends on the cultural norms and economic realities. Captured enhanced soldiers may be: ransomed (especially if nobility); killed (if they are expensive to replace); crippled and released (if they are expensive to replace and to discourage volunteers) etc
In summary, there would probably be very little difference in the conduct of warfare if the proposed potion enhancements were available. There would be a massive population explosion if the women were enhanced instead of the men though.
If such soldiers did exist, though, the "Duel on Boston Common" scene from the aforementioned film Highlander would probably be re-enacted frequently in the camps of less-disciplined armies. It just wouldn't be as funny.