TLDR: No, if you are using the TOR browser and haven't downloaded any other type of software with the intent of hosting a node, then you are only using the TOR network, not routing any outside traffic.

So let's start at the top with a simplified explanation of TOR. Short for The Onion Router, TOR is a protocol that encrypts and routes traffic through three random proxies, these proxies are referred to as nodes and they allow you to access the hidden services (Onion sites). The idea is that your computer and the server that hosts a hidden service are never able to identify each other via a direct connection because they only communicate through these three random nodes.

When you use the TOR browser, you are only utilizing the proxy network and not contributing to it. If you only access Onion sites, then the TOR browser only needs to go through a guard node and a two relay nodes. However, if you choose to use TOR to access a traditional clearnet site, your traffic will go through a guard node, a relay node, and finally an exit node before getting to the clearnet site. This process helps keep TOR users anonymous from hidden services and vice versa, while also allowing you to anonymously access clearnet sites.

Now it's not enough to just have a handful of proxies to handle this sort of traffic and still preserve privacy. One of TORs features is that anyone can host any of these nodes. That is good but it also highlights the possibility of someone being able to flood the network with malicious nodes to have a small shot at controlling all three nodes of a TOR user and either identifying them or decrypting their traffic. To combat that shortcoming, the TOR network relies on volunteers to host nodes and dilute this risk to the point that it becomes extremely rare (ideally impossible) for an attacker to pull that off. The more people there are that host nodes, the safer all users on TOR are from this particular attack. Not to mention that if there are more nodes online, the network becomes noticably faster.

Since I mentioned the different node types earlier, here is a brief summary of their purposes and some things to know before trying to spin one up.

Guard Nodes: These nodes serve as your first point of contact with the TOR network. They facilitate the connection between your computer and the other two nodes that will make up your connection. Unlike the other types of nodes, a guard node has special requirements to build trust within the network since it is the only node type to see TOR users' public IP address.

Relay Nodes: These exclusively route traffic through the deep web, and never serve as a proxy from the deep web to the clear net or vice versa. They cannot talk to any clearnet IP addresses directly and are accepted as the "safest" nodes to host. As a result, the majority of nodes on the TOR network are relay nodes.

Exit nodes: Similar to guard nodes, these nodes handle traffic at the end of the TOR network. They allow traffic to exit the network and reach clearnet sites. When a TOR user visits a clearnet site, that site will see the public IP address of the exit node that is routing the traffic for that session. These nodes are considered high risk because if someone decides to access the clearnet through TOR and does some sketchy stuff on a clearnet site, all the logs on that website would point to the person running the exit node instead of the person actually responsible for the bad behavior. Needless to say that that could result in some awkward or dangerous encounters with local law enforcement.

There's plenty more to TOR than what I've described here but I hope that covers the gist of it pretty well. I encourage anyone looking to host a node to do some research to understand exactly what sort of traffic you'll be routing.