Nodes are just pages, nothing else. Think of them as HTML pages in a browser.
Note that info does allow for global search, if anything searching is one of its main strengths over a bunch of HTML files in a directory, and it even allows both for arbitrary text search and for index-based search (where documents can place invisible index markers mid-text and searching for the text of markers as keywords you jump to the exact text position).
Of course this relies on the info viewer to implement. In the default GNU info viewer the / key does a search in the current page only, Alt-/ does a search in the current page and any pages linked as subpages (so you can do a search across pages but only at the current node - e.g. if you are in a book about a programming language and you are in the reference section you can search the entire reference, but ignore any tutorials or guides that may be placed in sections adjacent to the reference), i does a search in the index (here the prompt can do entry completion for you by pressing tab) and jumps to the appropriate entry and finally I (shift+i) does a search in the index and displays the results in a generated node (page) with links to each target (you can search this generated node using the / too).
Tkinfo provides similar functionality although i do not have an installation at the moment available to ensure (i'm under Windows where i have GNU info via msys2 but not tkinfo). Being a GUI application it does provide a few niceties like displaying the index and search results in separate windows and you also can choose to open links in separate windows (no tab support though).
I haven't used pinfo much, although IIRC from the little i used it (mainly to see how an info file i was working on looked there) despite it colorfulness it was a bit limited compared to other viewers.