From the perspective of a Second Life user, a typical roaming bot just comes and goes. They're typically on a region for less than a minute, and they don't interact with anyone or anything. Some try to stay "out of the way"—arriving at high altitudes, for instance—but most just land wherever they land. Sometimes one will get "stuck" or malfunction and stay on a region for some time. Most have a lower impact on sim resources and performance than a typical human-driven avatar.
Roaming bots are operated by Second Life users, not Linden Lab. There's a persistent myth some (or all) roaming bots are operated by LL to generate the inworld World Map (there's a historical coincidence that led to that theory). However, it's not true: as of October 2019, Linden Lab publicly confirmed that the World Map does not use any processes that would be visible to users inworld. Yes, the World Map was retooled in 2021 but not in a way that needs bots.
Under the Linden Lab Bot Policy, bots are allowed to do just about anything but buy mainland, spam users, and artificially inflate traffic statistics. Linden Lab requires bots be registered as "scripted agents," but prior to June 2023 SL users could not directly see if that flag has been set for an avatar. In early 2023 Linden Lab updated its bot policy to indicate it may "remove" scripted agents and supporting tools if "we see evidence of non-compliance with the Scripted Agent Policy or applicable privacy regulations." Basically, that means they can kill any bot(s) they like at any time for any reason, just like they do with regular residents.
My analysis of roaming bot activity since early 2019 strongly suggests many roaming bots are concerned with land ownership and/or other properties of inworld land, including the individual or groups that own regions and parcels, when those parcels change hands, and (in some cases) properties of the parcel like the ability to rez, object entry, ban lines, etc. This is information that can only be collected by sending an avatar to a region, and suggests many roaming bots are operated by virtual land dealers keeping an eye on the market (and competition). Virtual land is one of the few areas of SL where there's real money.
I'm fairly certain some roaming bots look for "exploitable" land: typically open-rez land that's held by old avatars who may not be in-world regularly, or land held by free-to-join groups with little or no activity, but which are free to join and provide rez rights to members. Bots can help identify exploitable land by pulling information on land ownership, group rights, last logins for residents, etc. I refer to parcels like this as "captive."
One group of roaming bots surveys mesh bodies, heads, and selected add-ons used by avatars they "see." Avatar accessories are a major portion of the SL economy—everyone has an avatar!—and various mesh body and head brands are among Second Life's biggest and most influential businesses.
My own bot (Loubottin) collects (fully anonymous) statistical info about avatars—height, memory used, script count, etc.
As of early 2022, one of the largest roaming bot cohorts is basically serving as an "assist" for playing an inworld game, roaming around and telling the operator(s) where other players of that game can be found. I'm not familiar with the game; presumably, proximity matters.
Some bots are associated with specific Second Life products (like Triple Labs' Explorer HUD) and others may be used by long-standing services like Tyche Shepherd's GridSurvey. A few others patrol public roads and waterways (likely mapping and/or checking for barriers to passage like overhanging builds or banlines); a handful more claim to be part of various mapping projects.
One bot operator has claimed to collect avatar names from estate and parcel whitelists/blacklists, as well as map individuals' group relationships between communities. I haven't yet substantiated that claim, but it's possible. Another has mentioned using a similar technique to identify various automated and semi-automatd avatars that target the various "free Lindens" traffic-generating games.
TL;DNR: Almost certainly not.
With enough bots, it's technically possible to try to track avatars around grid. However, besides being a violation of Second Life Terms of Service, such an effort would require a very large bot cohort. I would certainly notice them, and so would Linden Lab governance. None of the cohorts I'm tracking come close. In fact, the total number of grid-roaming bots I track doesn't come close. Yes, I know you might see bots all the time—as of early 2022 it's not unusual for regions to see a dozen visits a day, sometimes far more. But they aren't all operated by the same people or doing the same things. Upshot: I'm pretty sure this song isn't about you. Or me.
Moreover, someone with the technical skills to run a bot cohort could use other, more-effective ways to stalk Second Life users.
What about metadata? Could a group of bots teleporting around the grid build up a database of locations where particular avatars have been seen and generate a graph of potential connections between them? Yes: that's possible within some limits. First, grid-roaming bots can't go everywhere: bots get banned all the time (more often now that scripted agents are directlyu detectoable). There also lots of private/restricted regions where bots simply cannot go. Second, unlike beacons used by Internet companies like Facebook, Amazon, and Google that automatically track people all around the Internet (often without users realising it), bots actually have to get in the same region as avatars to detect them. Second Life isn't really very large, but most people spend only a few hours inworld at a time. The potential data available to a group of bots is always going to be piecemeal and incomplete. But yes: over time, a group of bots could build up location and association profiles of avatars from publicly accessible information.