You may of entered a typo in your post, but it should be user:pass@manager-url/api/
Also do you have curl installed?
I have Windows 10 running DeskTop version and WSL with ubuntu 18.04 running mono and manager-server (set to use port 8123).
curl --ipv4 -v --get "http://administrator:@localhost:8123/api/index.json"
returns
* Trying 127.0.0.1...
* TCP_NODELAY set
* Connected to localhost (127.0.0.1) port 8123 (#0)
* Server auth using Basic with user 'administrator'
> GET /api/index.json HTTP/1.1
> Host: localhost:8123
> Authorization: Basic YWRtaW5pc3RyYXRvcjo=
> User-Agent: curl/7.61.0
> Accept: */*
>
< HTTP/1.1 200 OK
< Cache-Control: no-cache, no-store
< Content-Type: application/json
< Server: Mono-HTTPAPI/1.0
< Date: Wed, 12 Aug 2020 10:02:50 GMT
< Content-Length: 314
< Keep-Alive: timeout=15,max=100
<
[
{
"Key": "VGVzdGluZzAwMQ",
"Name": "Testing001"
},
{
"Key": "VGVzdGluZzAwMg",
"Name": "Testing002"
},
{
"Key": "VGVzdGluZzAwMw",
"Name": "Testing003"
},
{
"Key": "VGVzdGluZzAwNA",
"Name": "Testing004"
},
{
"Key": "Tm9ydGh3aW5k",
"Name": "Northwind"
}
]* Connection #0 to host localhost left intact
Then looking at an invoice for Northwind…
curl --ipv4 -v --get "http://administrator:@localhost:8123/sales-invoice-view.json?FileID=Tm9ydGh3aW5k&Key=4850f691-6abc-41d1-8e7a-3e8b5662db56"
which returns:
* Trying 127.0.0.1...
* TCP_NODELAY set
* Connected to localhost (127.0.0.1) port 8123 (#0)
* Server auth using Basic with user 'administrator'
> GET /sales-invoice-view.json?FileID=Tm9ydGh3aW5k&Key=4850f691-6abc-41d1-8e7a-3e8b5662db56 HTTP/1.1
> Host: localhost:8123
> Authorization: Basic YWRtaW5pc3RyYXRvcjo=
> User-Agent: curl/7.61.0
> Accept: */*
>
< HTTP/1.1 200 OK
< Cache-Control: no-cache, no-store
< Content-Type: application/json
< Server: Mono-HTTPAPI/1.0
< Date: Wed, 12 Aug 2020 09:45:41 GMT
< Content-Length: 1253
< Keep-Alive: timeout=15,max=100
<
{"title":"Invoice","description":null,"reference":"3002","emphasis":{"text":"Overdue","positive":false,"negative":true},"fields":[{"label":"Invoice date","text":"8/9/2020","emphasis":false},{"label":"Due date","text":"8/9/2020","emphasis":false},{"label":"Invoice number","text":"3002","emphasis":false}],"custom_fields":[],"table":{"columns":[{"label":"Description","align":"start","nowrap":false},{"label":"Qty","align":"center","nowrap":true},{"label":"Unit price","align":"right","nowrap":true},{"label":"Amount","align":"right","nowrap":true}],"rows":[{"cells":[{"value":null,"text":"14/07/2020 - Testing"},{"value":3.25,"text":"3.25 hours"},{"value":14.25,"text":"14.25"},{"value":46.31,"text":"46.31"}]},{"cells":[{"value":null,"text":"20/07/2020 - "},{"value":null,"text":" "},{"value":125.0,"text":"125.00"},{"value":125.0,"text":"125.00"}]}],"totals":[{"label":"Total","text":"$ 171.31","number":171.31,"emphasis":true}]},"business":{"logo":"/business-logo-view?Key=4f6ce09d-d6f8-4ce5-bf3e-163718d7c263&FileID=Tm9ydGh3aW5k","name":"Northwind","address":null,"custom_fields":[]},"recipient":{"code":null,"name":"Around the Horn","address":"120 Hanover Sq.\r\nLondon NULL WA1 1DP\r\nUK\r\n","identifier":null,"email":null,"telephone":null}}* Connection #0 to host localhost left intact
Your error seems to indicate it may be an authentication error
I agree in regard to &Term=*some-filter* does not work. It would be really helpful if it did 
, I just delete the one with red color and everything works fine now.