Nothing to troubleshoot -- the URIs (which are, as per the name, identifiers, not links) don't work as links because they were abused for spam (I believe).
I don't believe you can create links from the local app programmatically, but you can obviously use search & replace (including in a script) to do so for your library specifically

With Obsidian Zotero Data Explorer and Prompt for Selection, and selecting one item in with Zotero, I got a list of all possible template data. Then I found
key "2EUEMSPD"
uri "http://zotero.org/users/12341234/items/2EUEMSPD"
where 12341234 has been changed here.

In My Zotero template.md, I have now
[Zotero online with uri]({{uri}})
[Zotero online with username and key](https://www.zotero.org/JOEX/items/{{key}}/)
where JOEX should be replaced with your user name.

The first links does not work, same as above. The second link works now for a few items I have tried.

I use
Zotero 7.0.11
Better BibTex for Zotero 7.0.2
Obsidian v1.7.7
Zotero Integration plugin 3.2.1

Here is the complete zotero_template.md I use now (replace JOEX with your zotero username)

## {{title}}
- Authors: {{authors}}
- Year: {{date | format ("YYYY")}}
- ItemType: {{itemType}}
- Abstract: {{abstractNote}}
- Sources:
- [Zotero online with uri]({{uri}})
- [Zotero online with username and key](https://www.zotero.org/JOEX/items/{{key}}/)
- [Zotero local]({{desktopURI}}) {%- for attachment in attachments | filterby("path", "endswith",".pdf") %}
- {{pdfZoteroLink}}
- [pdf file attachemnt](file:///{{attachment.path | replace(" ","%20")}}) {% if loop.last %}{% endif %}{%- endfor %}
- Bibliography: {{bibliography}}
- Cite Key: [[{{citekey}}]]
{%- if hashTags %}
- Tags: {{hashTags}}
{%- endif %}

Thanks, I made a correction above. It should be {{pdfZoteroLink}} and not [Zotero link pdf]({{pdfZoteroLink}})