Logging Out of Dell Community Does Not Log Me Out of My Dell Account

If I log out of this Dell community and then visit another Dell web page (e.g., https://www.dell.com/support/home/en-us?app=products) during the same browser session I can see that I am still logged in to my Dell Account and have to log out a second time.

To reproduce the problem:

1. Browse to this Dell community at https://www.dell.com/community/en/categories/dell-community and confirm you are signed out.
2. Open a new browser tab and browse to https://www.dell.com/support/home/en-us?app=products (Note: I live in Canada and am automatically re-directed to https://www.dell.com/support/home/en-ca/products) and confirm you are signed out. Close this browser tab.
3. Sign in to the Dell community at https://www.dell.com/community/en/categories/dell-community.
4. Sign out of the Dell community. Close this browser tab.
5. Open a new browser tab and browse back to https://www.dell.com/support/home/en-us?app=products.

Expected result: I should be signed out of my Dell Account.

Actual result:   I am still signed in to my Dell account (see image below) and must sign out a second time.

I have confirmed this behaviour is reproducible in both my Firefox (default) and MS Edge browsers.

I have discovered that I avoid this problem if I close my browser after I sign out the Dell community (Step # 4), which I assume is because both my Firefox and MS Edge browsers are configured to clear my browsing history (including cookies) on exit.  If I close my browser after signing out of the Dell community in Step # 4, restart my browser, and then browse back to https://www.dell.com/support/home/en-us?app=products (Step # 5) I can see I am correctly signed out of my Dell Account.

EDIT:

I have also noticed that if I (supposedly) log out of this Dell community and then browse back to the community later in the same browser session that I am still logged in.

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Dell Inspiron 15 5584 * 64-bit Win 10 Pro v22H2 build 19045.4780 * Microsoft Defender v4.18.24070.5-1.1.24070.3 * Malwarebytes Premium v5.1.9.124-1.0.5014 * Macrium Reflect Free v8.0.7783 * Firefox v129.0.2 * Microsoft Edge v128.0.2739.54 * * Dell Update for Windows Universal v5.4.0 * My Dell v2.2.6.0