The number you are looking for is not Dunbar's Number
Dunbar's number is about how many relationships you can maintain, but does not directly dictate the "sense" of knowing everyone. Another relevant figure is that the average person can recognize 5000 people's faces; so, as long as you recognize everyone you encounter, and know enough of them to feel compelled to engage with someone everywhere you go, then the "sense" of knowing everyone is preserved.
This means that the actual size you are looking for is going to be somewhere between 150-5000 (if not higher), but where it that range it falls will depend a lot on various practical and cultural factors.
First of all, how many people you can know is not so much how many people there are, but how many people you must interact with. Even in a small town, most people only know their immediate neighbors plus people who they share a joint activity with. The key here is the joint activity. Generally speaking, the 4 joint activities that bind small towns are a single school, a single church, a single industry, and/or a single popular recreation. If you have all 4, then you will generally be able to connect with enough people from at least 1 of these places to always feel like you know someone everywhere you go.
For a school to really create this effect, it is best to have a 1 class per grade structure which maxes at about 30 students per grade level. Since ~18% of the World's population are school aged children, and they can be divided into 12 Grade Levels. This means that each grade represents about 1.5% of your total population; so, a single class/grade school system can support a total population of about 2000 people. This would guarantee that you would know everyone in your own generation, and probably most of the children and parents of children in your children's generations. While this is not enough to actually know everyone in town, people tend to congregate in places that are popular within their own generation; so, if everyone in the same high school class used to go to the same diner as kids, then as adults, they will likely continue to go there and continue to run into the same people over and over again strengthening the sense that they know everyone.
Churches are generally better than schools at uniting people between different generations and backgrounds than jobs or schools, but they tend to make who you connect with much more optional. As such, you tend to see that churches with congregations bigger than Dunbar's Number do often form many smaller communities of acquaintances rather than a single unified church community. So, a church will generally not help you know everyone well in a larger town better, it can help connect you with generations of people you would otherwise not know. If a church is the only unifying factor your town has, then your limit may in fact be closer to Dunbar's Number, but when paired with other unifying factors, their ability to form cross generational relationships may make you feel more like you know everyone, because you will internalize that you know people outside of your inner circle.
Like churches, these can do a good job of bringing together on the scale of Dunbar's Number before some of the people you share a work area with are just strangers to you. However, unlike a church, there is not as big of a spread of demographics since you will only be working with people of working age. This can leave bigger gaps in who you do not know, but also serve more as a linchpin to become familiar with more people indirectly.
The fewer popular recreations there are in an area, the more likely you are to have a shared interest with someone who is otherwise a stranger. Let's take American football for example. In many small American towns you do not need to really know someone to start talking to them about the the local football team. One of the biggest elements of feeling like you know everyone is having a common language for breaking the ice when you do encounter someone new (or who you only know by face), and common recreation is great for that. So, sit down next to a stranger and they lean over and ask if you saw the game last weekend, you answer "yes", and you start to talk about it. You don't really know that person but you maintain the feeling that you kinda do because you have a shared experience to discuss.
This leads into the final key to this question which is how people process the sense of knowing everyone. Human nature works on the pieces of information we choose to process and not the information we choose to ignore; so, you only need to know 1 person wherever you go, and not spot too many people you do not recognize at all to feel like you "know everyone".
So, if every time I go somewhere and there are 20 familiar faces, a couple of total strangers, and just 1-2 people I actually know on a personal level, this is good enough to maintain the sense of knowing everyone.
The real wild card here is population density though. 100/sqmi is a very low density. There will not be enough people in small enough of an area for you to want to be regularly going places you might meet people; so, out of a town of 2000, most people will stick to smaller sub communities and seem like random strangers on the rare occasion you do see them out in the world, but if you were to cram 2000 people into small town center, it is much more likely that you will recognize most of those 2000 people.