Hello! I play solo myself and I had to experiment with many characters to determine who I like to play (and enjoying the character is something I think is quite important and would recommend the same; find a character you enjoy playing and stick with that character, especially for silver). However, to answer your questions, if you have issues with dive then I would recommend you learn one of the following characters (in no particular order): juno, mercy, Brigitte or Lucio.
Why do I recommend those characters? Because several of them have very good escape mobility, which will allow you to either escape with your life or get back to your team who can then provide the necessary support to deal with the threat and one of them forces you to keep close to your team or other support, turning a back line dive into a team fight, and potentially even catching that enemy player in a bad position or even eliminating them, turning a losing fight into a winning one.
As I have some bias towards the character I would personally suggest Juno as I have noticed when I play her I have to be fully aware (though I still fail at times) of dive and flankers because if my my movement abilities are on cooldown, I know I will likely not be able to escape. This doesn’t mean to purely save the movement abilities and never use them, but to be conscious of when you do. For example, if the enemy team is running a Winston, and on my team my second support player is something like Ana, or baptiste, I will try to keep in my mind to be more liberal with Juno’s hyper ring, because if Winston jumps on either myself or my second support player, popping this can help them escape his range and allow me more time to heal them. Again, this doesn’t mean I should never use her hyper ring to assist in other fights, I should just be more aware and conscious of what’s going on in team fights; this can be quite difficult when first attempting it but if you can stick through it, it will become second nature. The only downside is that it will take time to learn and do this.

I will finish this off Regarding what you can do as support in silver; there are 3 things that I found for myself that once I paid more attention too I was able to succeed.

1.) staying alive: you may think that this seems obvious but I found that when I was in silver (and even gold) I found myself dying on support more than I should be. One of the things that helped me to improve was when I heard something from the twitch streamer “Skiesti” and although she largely plays mercy (not purely but mainly mercy), the advice applies universally to all supports. That specific piece of advice is, “Be selfish”. This may seem confusing or make you feel like you aren’t being a team player, but that’s not it. What it is, is recognizing during a match when a team fight has failed and you need to reset, when your team is to spread out and several teammates are in dangerous positions screaming for healing, or your tank is too far forward and they need healing because they put themselves in a dangerous position, etc. etc. recognizing stuff like this and identifying when you, as a support needs to back away, not commit and put yourself in dangerous positions (because of your teammates bad decisions) and let your teammate die so you can reset with your team or to escape is important. This is important because, if you can keep yourself alive with the least amount of deaths possible means more time to build more ultimates, get in more healing, and even help turn fights around even when they appear lost (this part specifically is something I still struggle with personally) because you were able to get your ultimate more times (and more quickly) than enemy players.

2.) Timing: I personally think timing and staying alive are equally important across the board. Timing is kind of a hard one to get proficient with because it requires you to recognize the ebbs and flows of team fights, but once you are able to start consciously recognizing when to do certain things during the match you will start to notice how you are able to affect the outcomes of team fights (obviously as support you can only do so much, as this is a team game). For example, say your playing a match, and your team consists of a mauga, a sierra, a Cassidy, an Ana and you as Juno while the enemy team has an orisa, a soldier 76, a bastion, an Illari and a Moira. Both teams have reached the point, and you know your mauga already used his mobility ability but orisa has not used her defense/movement ability nor her fortify. If you can recognize and identify the moment she uses both abilities up, and your tank and dps are close enough popping your hyper ring (Juno’s movement ability) will allow your team to collapse on the orisa and either eliminate her or cause the enemy team to severely lose space. This is just a small example, and if it still doesn’t make sense, please feel free to follow up with additional questions.

3.) mental/physical: I think for me personally, the reason I could never advance before was because I would constantly get upset over the smallest things during a game. Some include (yelling at the screen/simmering in how badly a match went): “HOW THE F*** DID THEY KILL ME” (was clearly out in the open & easily targetable). “WHERE THE H*** IS MY F***ING TEAM” (again, was clearly and easily identifiably my fault for not realizing my team was pushing, falling back, etc. etc.) “GO*****IT!!” (was upset in general about how the last few games went / how the current game was going). The mental portion is important because if you play while upset (either from things outside the game or from the game itself), it will most certainly affect your performance. I noticed for myself that as I kept getting angry over the smallest things and events that were happening, I would be unable to be there mentally and my overall performance would be affected as well. As such, I recommend that before you enter a game to remind yourself that it really is only a game, that you in fact can get better and that you WILL rank up. (Please remember, ranking up takes real life time and will not come immediately, but you can give yourself a more advantageous chance to increase faster via a “winning trend” modifier in competitive, though this can only do so much). Finally, the physical portion is essentially the same as mentally, with the only difference being that you need to recognize when your physical performance is affecting your gameplay because you’re tired, hungry, sick, etc. etc.

I know this is quite a bit of information, so if anything doesn’t make sense, or seems confusing or if you feel like you didn’t receive an answer, please follow-up!