A heuristic guess is: not impossible, but towards the lower end of probability.
Grab packet capture software for your system,
(1) limit it to the IP address of the laptop and see what you receive when it boots. Port scans are very easy to distinguish by the sheer number of packets sent towards different ports with no clear reason. A typical port scan will use SYN packets, without ever attempting to actualy make a connection. Wikipedia describes
common port scan methods, but it’s unlikely it would be anything fancy — in particular for unattended scan.
Some types of software try to scan LAN for various services without any harmful intents. That includes both things installed on a computer and firmware in “smart” TVs and such. Such an attempt may trigger alarms in antivirus software. That’s typically easy to distinguish from a port scan,
(2) because packets arrive only to a small number of relevant ports (e.g. belonging to Spotify servers in case of “smart” TVs).
But, in general, the situation raises a very important concern. That you are running an operating system that was used by someone else in the past, instead installing it from scratch. That is always a security risk.
(1) Wireshark is a common program of that type that works across multiple platforms.
(2) To an intelligent beaing, not to an automated system — unless it
knows specific rules describing that kind of traffic.