Does the WTO itself have any input into trade agreements, or is it merely a forum for sovereign states to negotiate and settle disputes?
No. The WTO as an organisation doesn't make decisions. Countries do not delegate decision making power to the WTO as an organisation, a 'forum' is a pretty good description, if one is only talking about trade negotiations.
The WTO has more power than just a forum, however, when it comes to arbitrating existing agreements.
The WTO describes itself as a:
"a rules-based, member-driven organization—all decisions are made by the member governments, and the rules are the outcome of negotiations among members"
There are multiple committees, but the one you're probably interested in is the Trade Negotiations Committee. Like the others, it is made up of representatives of each country.
- Negotiations shall be open to:
(i) all members of the WTO; and
(ii) States and separate customs territories currently in the process of accession and those that inform members, at a regular meeting of the General Council, of their intention to negotiate the terms of their membership and for whom an accession working party is established.
Decisions on the outcomes of the negotiations shall be taken only by WTO members.
The closest thing to someone "representing the WTO" is the chairperson of these committees. But their role is to facilitate and help the members reach consensus. All decisions are taken by the members.
Where the WTO is more powerful than a forum is in dispute