I'm reading Peter Wilson's The Thirty Years War: A Sourcebook and it mentions various nations that were invited to sign the Treaty of the Hague, including the King of Sweden, the Prince of Transylvania, the Duke of Savoy and various other German officials are invited.
And so was the "Serene Republic of Venice". They seem like a bit of an outlier from the rest. Being predominantly Catholic, but unlike France, without any obvious interest in a war in the Holy Roman Empire, so what prompted the initial signers of the Treaty of the Hague to invite the Republic?
You should view it in the context of the greater anti-Habsburg politics.
The 1625 meeting in The Hague was intended to build a large anti-Habsburg alliance not only in northern Germany but also in the southern flanks. But because various parties declined to participate, the list of participants appears "strange" but it is really "incomplete".
In order to send troops to Germany and the Low Countries, the Spanish Habsburg needed to control a route through Italy. This put both Savoy and Venice, in that timeline, against Spain. The 1625 Treaty of The Hague was negotiated in the shadow of implicit French assistance to Savoy as it attacks Genoa who was a strong Spanish ally, and to Venice as it attacks Milan which was a Spanish dominion. In late 1624, prior to The Hague goal of the allies was to enlist both Denmark and Sweden, and with French and English support, alongside belligerents Venice, Savoy, Brandenburg, Brunswick, Bohemia, Palatine, Saxony, etc etc etc.
Unfortunately for the belligerents, Sweden couldn't agree on France's participation, and Denmark literally jumped the gun. Christian IV of Denmark entered the war in early 1625 foolishly prematurely according to Christian's own advisors, even though at the time the "Protestant" camp felt strongly that they needed a grand alliance.
Not wanting to play second fiddle, the Swedes under Gustavus Adolphus had decided to focus on their war against Poland in summer 1625, plus relations between Sweden and Denmark were not great at that point. So what was hoped to be a grand alliance of anti-Habsburg powers were missing key players such as Sweden, and further Pomerania and Saxony as they felt vulnerable when Sweden abandoned them.
In short, Denmark entered war by itself prematurely, even with funding provided by France who was still staying out of active participation. To make things worse, the siege of Breda was won by the Spanish, whose troops are now free to oppose Denmark. We now know that by the following year, Denmark paid for it as they were soundly defeated in Lutter in 1626. Even worse, the most loyal Danish troops were the ones who suffered the worst casualties due to their steadfastness in the face of slaughter by Imperial troops. This basically turned Denmark into a non-important military player even though their funding was still useful.
So by the time the meeting in The Hague was called in November 1625, it was a rather smaller alliance, and grimmer prospect, than they had previously hoped. That's what explains the participants' list, it's not "strange", it's "incomplete".
Sources: Geoffrey Parker's "The Thirty Years War", and parts from Peter Wilson's "The Thirty Years War: Europe's Tragedy".