Unresponsive or failed internet connections when connected to Tailscale

### What is the issue?

When connected to Tailscale, not using an Exit Node, the internet connections on my iPhone, Macs, and Linux desktop will regularly stall or fail. This has been going on for at least two weeks so it would have started with Tailscale v1.102.2. When initiating web searches and connecting to websites for the first time pages take an extra approximate 5 seconds to load, or they will fail on first attempt. Loading is always faster or succeeds after the first time.
If the Tailscale connection is disabled network performance returns to normal. Normal as in not failing to connect to websites, webpages loading at the expected speed, etc. This also has effected things like Fedora repos. When running `dnf upgrade` the PC will either fail to connect to repos on the first attempt or will take longer than usual.

### Steps to reproduce

1. Connect to Tailscale
2. Open a web browser (Firefox, Safari, Chromium, etc.)
3. Open a private window so caching doesn't affect performance
4. Initiate a web search from the address bar

Tailscale ON = increased time to load result OR failure to load on first attempt
Tailscale OFF = expected performance based on network speed (500Mbps up and down)

### Are there any recent changes that introduced the issue?

_No response_

### OS

macOS, iOS, Linux

### OS version

macOS 15.7.8, iOS 27 Public Beta, Fedora KDE 44

### Tailscale version

1.102.3

### Other software

On macOS and iOS iCloud Private Relay is active, on Linux there is no additional networking or security software running.

### Bug report

BUG-dec753ffcce59694066e1472f7078bf150d1387837783fefb728f331ea1ed0d7-20260827135057Z-37c78e9c0314d17d

Start by reproducing the first-request delay and failures on macOS, iOS, and Fedora with Tailscale 1.102.3 enabled and disabled, using a private browser window and a Fedora repository update. Done means initial web and repository connections perform normally while Tailscale remains enabled; the payload names no source files or tests to inspect.

Written by the indexing model from the issue text.