Not all problems are visible even though background analysis mode is set to full solution

Type: Bug

## Issue Description ##
Often when accessing problems view I see problems only for some files. It's often the case that when I go through problems with arrows and different files open, other problems disappear.
And sometimes when I close all files I get empty problem list.
It's even though my solution is quite small, and I have the background analysis mode set to full solution.
Oh also trying to use fix all code action for whole solution pretty often doesn't fix all solution. Unsure if it's related to currently visible problems or not.

## Steps to Reproduce ##
I don't understand this issue enough to reproduce and it might even be it's expected behavior for some reason, however
That requires background analysis to be set to "full solution". Basically try opening a solution with problems and start clicking on them to open different files and see what happens.
Or make sure you will actually see all of them.

## Expected Behavior ##
I expected to see all problems for a small solution. I definitely don't reach the problem limit.

## Actual Behavior ##
Problems are initially visible but then disappear randomly from my perspective.

## Logs ##

### C# log ###
Post the output from Output-->C# here

### C# LSP Trace Logs ###
Post the output from Output-->C# LSP Trace Logs here. Requires the `C#` output window log level to be set to `Trace`

## Environment information ##

**VSCode version**: 1.104.0-insider
**C# Extension**: 2.87.31
**Using OmniSharp**: false

Dotnet Information
.NET SDK:
Version: 9.0.303
Commit: 5d97611193
Workload version: 9.0.300-manifests.fadeff71
MSBuild version: 17.14.13+65391c53b

Runtime Environment:
OS Name: ubuntu
OS Version: 24.04
OS Platform: Linux
RID: linux-x64
Base Path: /usr/share/dotnet/sdk/9.0.303/

.NET workloads installed:
There are no installed workloads to display.
Configured to use loose manifests when installing new manifests.

Host:
Version: 9.0.7
Architecture: x64
Commit: 3c298d9f00

.NET SDKs installed:
9.0.303 [/usr/share/dotnet/sdk]

.NET runtimes installed:
Microsoft.AspNetCore.App 9.0.7 [/usr/share/dotnet/shared/Microsoft.AspNetCore.App]
Microsoft.NETCore.App 9.0.7 [/usr/share/dotnet/shared/Microsoft.NETCore.App]

Other architectures found:
None

Environment variables:
DOTNET_ROOT [/usr/share/dotnet]

global.json file:
Not found

Learn more:
https://aka.ms/dotnet/info

Download .NET:
https://aka.ms/dotnet/download

Visual Studio Code Extensions

|Extension|Author|Version|Folder Name|
|---|---|---|---|
|copilot|GitHub|1.356.1735|github.copilot-1.356.1735|
|copilot-chat|GitHub|0.31.2025081401|github.copilot-chat-0.31.2025081401|
|csdevkit|ms-dotnettools|1.41.11|ms-dotnettools.csdevkit-1.41.11-linux-x64|
|csharp|ms-dotnettools|2.87.31|ms-dotnettools.csharp-2.87.31-linux-x64|
|gitlens|eamodio|17.3.4|eamodio.gitlens-17.3.4|
|markdown-preview-enhanced|shd101wyy|0.8.19|shd101wyy.markdown-preview-enhanced-0.8.19|
|vscode-dotnet-runtime|ms-dotnettools|2.3.7|ms-dotnettools.vscode-dotnet-runtime-2.3.7|
|vscode-github-actions|github|0.27.2|github.vscode-github-actions-0.27.2|
|vscode-github-issue-notebooks|ms-vscode|0.0.133|ms-vscode.vscode-github-issue-notebooks-0.0.133|
|vscode-pull-request-github|GitHub|0.116.1|github.vscode-pull-request-github-0.116.1|
|vscode-yaml|redhat|1.18.0|redhat.vscode-yaml-1.18.0|
|vscodeintellicode-csharp|ms-dotnettools|2.2.3|ms-dotnettools.vscodeintellicode-csharp-2.2.3-linux-x64|
|xml|DotJoshJohnson|2.5.1|dotjoshjohnson.xml-2.5.1|;

Extension version: 2.87.31
VS Code version: Code - Insiders 1.104.0-insider (97bc9a439c022a88fba7be68f67e068361f6c467, 2025-08-12T17:22:21.373Z)
OS version: Linux x64 6.15.9-201.local.fc42.x86_64
Modes:
Remote OS version: Linux x64 6.15.9-201.local.fc42.x86_64

System Info

|Item|Value|
|---|---|
|CPUs|12th Gen Intel(R) Core(TM) i7-12700H (20 x 3621)|
|GPU Status|2d_canvas: enabled
direct_rendering_display_compositor: disabled_off_ok
gpu_compositing: enabled
multiple_raster_threads: enabled_on
opengl: enabled_on
rasterization: enabled
raw_draw: disabled_off_ok
skia_graphite: disabled_off
trees_in_viz: disabled_off
video_decode: enabled
video_encode: disabled_software
vulkan: disabled_off
webgl: enabled
webgl2: enabled
webgpu: disabled_off
webnn: disabled_off|
|Load (avg)|1, 1, 1|
|Memory (System)|31.05GB (20.40GB free)|
|Process Argv|--crash-reporter-id d631c74a-e6b8-4995-a801-c11d60474935|
|Screen Reader|no|
|VM|0%|
|DESKTOP_SESSION|gnome-xorg|
|XDG_CURRENT_DESKTOP|GNOME|
|XDG_SESSION_DESKTOP|gnome-xorg|
|XDG_SESSION_TYPE|x11|

|Item|Value|
|---|---|
|Remote|Dev Container: discordsharp-env @ rootless|
|OS|Linux x64 6.15.9-201.local.fc42.x86_64|
|CPUs|12th Gen Intel(R) Core(TM) i7-12700H (20 x 3470)|
|Memory (System)|31.05GB (20.41GB free)|
|VM|0%|

A/B Experiments

```
vsliv368:30146709
pythonvspyt551cf:31249598
nativeloc1:31118317
dwcopilot:31158714
dwoutputs:31242946
copilot_t_ci:31333650
g012b348:31231168
pythoneinst12:31251391
6gi0g917:31259950
996jf627:31264550
pythonrdcb7:31268811
usemplatestapi:31297334
747dc170:31275146
pythonpcpt1:31345880
6518g693:31302842
9d2cg352:31346308
j97ad248:31349650
usemarketplace:31343026
0g1h6703:31329154
82j33506:31327384
nes-emitfast-1:31333560
replacestringexc:31350595
6abeh943:31336334
envsactivate1:31349248
0927b901:31340060
nb18600_tf:31359574
1je7-usegpt41:31345955
editstats-enabled:31346256
gendocstringt:31358906
pylancealldocst:31362265
cloudbuttont:31366566
todos-1:31366868
search_len_ctrl:31367734
multireplacestring:31368509

```