Assuming the account provides "value" and high number of followers, profile links are huge and I assume at least 10% of those people will click the link in the bio to your website. It seems people like to read the 140 word message and see the picture associated with the tweet but most are not keen on clicking the link in a tweet.
Is it your findings or what's the source?
I'm asking, because generally in terms of engagement, tweets with urls outperform tweets without urls. And it's not just about visitors how likely click on a link, but tweets with urls are more attention grabbing and even if the visitor doesn't click on a link, there's a higher chance to engage (retweet/like/reply) with a tweet with url opposed to a tweet without url.
My source for some of this is RiteTag and my own findings, which seem to correlate with each other.
^ Perhaps you can tell us some tips on achieving number (3).
What do you mean by this? Because to achieve that, in a nutshell you only need to tweet and appear in Twitter search, because that's when those people - who aren't your followers - can see your tweets.
One trick is to use proper hashtags and not to get ghosted for spamming, which is the hard part. lol Another trick is when you have a small army of Twitter accounts and you can generate real-looking but not so real engagement (retweet/like) for your tweets, hence they will rank higher in Twitter search, so people can actually find them, when they are looking for certain keyword(s)/#hashtag(s).
quick tip, put the URL in the profile after you have some sort of confirmation that your setups won't get your account banned.
Generally it's a wise advise, however i don't find this necessary on Twitter just yet. According to my findings when i work with brand new accounts, i can add an url right to the website field from the beginning, the url doesn't disappear on any device, it doesn't make the account locked or affect the account negatively in any other way, with that said, i use one domain per account, i never cross-promote. Of course the url cannot be blacklisted.
Answering to OP: It can be just a bug-like issue connected to accounts, which got hit with a password reset/phone lock and either haven't been unlocked yet or were unlocked just recently. For instance when an account gets locked, most of the time the number count of following disappears, not the followings, just the number, after you unlocked the account, it re-appears, not right away, but after a while (few hours). So it's more like a thing Twitter does to locked accounts (as a punishment).
But maybe it's not it, because i just checked with a non-locked, a phone locked and a password locked account too and i can't see this happening with the url neither on desktop nor on Android with any of those accounts, so i guess there must be another explanation, i'm not aware of.