The only mistake you made was the choice of cut, and maybe the quality of the beef itself. Round (in the UK/AU/NZ topside and silverside) is from the rear end of the animal, and is a working cut. Working cuts have to exert a force, so the muscle must have lots of collagen to distribute the force from the tendon throughout the muscle. Collagen is a tough material which breaks down in the presence of heat and moisture, not just heat, so working cuts make poor roasts or steaks and are better braised or stewed.
The upside to working cuts is that they have a stronger flavor, and the collagen when broken down by moisture turns to gelatin which adds to the flavor and mouth feel. A well-prepared braised piece of beef is as good as a roast any day in my opinion. It's also better value, round and other working cuts are much cheaper than tender cuts.
Your technique as described is perfect, and if you'd chosen a rib, short loin, or sirloin roast (US cuts) it would have come out beautifully. Where you erred was at the store when you chose a working cut for roasting.
Now some people on the forum are probably preparing a rebuttal at this point saying "you can roast round and have it be tender", and they'd be right up to a point. The best quality beef is reared and slaughtered better, so if you bought US Prime round it has a good chance of coming out relatively tender, however it's hard to find. My assessment would be for what you'd find in the average store in the US, which is Choice grade. Choice encompasses something like 75% of beef produced, so has a huge range of quality.
You can tell a lot about meat by touching it. Stick your fingers in it, if they go in easy and the meat springs back then you have a tender cut, if you can't get your fingers in it it's a braising cut. If you stick your fingers in and the meat doesn't spring back its old, so don't buy it.
Yes, a simmer will be on the order of 180 to 200 F (82 - 93 C) which is a safe temperature for cooking and holding stew.
Browning beef does cook it, but usually not all the way through as that is not the point; instead it is to develop the flavors. The full cooking is done during the braising or stewing stage while you simmer it. This also allows the collagen to hydrate into gelatin, creating the tender texture of well cooked stew meat.
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Unless you are getting your beef directly from a farm or butcher's truck, most blood will long have vacated the muscle. As the muscle enters rigor mortis and is (this is true for America and Europe, traditions and techniques are different in some parts of Asia and Africa) hung for the prescribed seven to ten days it loses almost all of its capillary blood.
Dry aged (not as common) beef has this effect even more, if you purchased a supermarket filet with a "sanitary pad" in the bottom, the moisture you see there is juices, water and some protein, from collapsing cells, not blood. The same is true for any beef not cooked to shoe-leather consistency, the reddish "juice" is intra-cellular and not from blood vessels.
As far as flavors go, soaking your meat for any period of time below, let's say, two days, has very little effect. It was traditionally done to apply some osmotic power to the cut in order to dilute and remove salt left over from the drying process (this was before cooling was widely available, still done in many countries outside of Europe and America), but isn't usually necessary for meat you get in the meat aisle or from your local butcher.
As far as tenderizing goes, no. Enzymatic tenderizing (that is the stuff that happens when you age beef) goes on, of course, but you won't be able to tell much of a difference between the time you bought the muscle and the time you consume it. Water itself does not tenderize. Minutes to hours do nothing.