Can I use
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Session history management

- LS

Method of manipulating the user's browser's session history in JavaScript using history.pushState, history.replaceState and the popstate event.

Chrome

  1. 4: Not supported
  2. 5 - 123: Supported
  3. 124: Supported
  4. 125 - 127: Supported

Edge

  1. 12 - 122: Supported
  2. 123: Supported

Safari

  1. 3.1 - 4: Not supported
  2. 5 - 5.1: Partial support
  3. 6 - 17.3: Supported
  4. 17.4: Supported
  5. 17.5 - TP: Supported

Firefox

  1. 2 - 3.6: Not supported
  2. 4 - 124: Supported
  3. 125: Supported
  4. 126 - 128: Supported

Opera

  1. 9 - 11.1: Not supported
  2. 11.5 - 108: Supported
  3. 109: Supported

IE

  1. 5.5 - 9: Not supported
  2. 10: Supported
  3. 11: Supported

Chrome for Android

  1. 123: Supported

Safari on iOS

  1. 3.2 - 4.1: Not supported
  2. 4.2: Partial support
  3. 5 - 17.3: Supported
  4. 17.4: Supported
  5. 17.5: Supported

Samsung Internet

  1. 4 - 23: Supported
  2. 24: Supported

Opera Mini

  1. all: Not supported

Opera Mobile

  1. 10 - 11: Not supported
  2. 11.1 - 12.1: Supported
  3. 80: Supported

UC Browser for Android

  1. 15.5: Supported

Android Browser

  1. 2.1: Not supported
  2. 2.2 - 2.3: Supported
  3. 3 - 4.1: Not supported
  4. 4.2 - 4.4.4: Supported
  5. 123: Supported

Firefox for Android

  1. 124: Supported

QQ Browser

  1. 14.9: Supported

Baidu Browser

  1. 13.52: Supported

KaiOS Browser

  1. 2.5: Supported
  2. 3: Supported

Older iOS versions and Android 4.0.4 claim support, but implementation is too buggy to be useful.

Resources:
MDN Web Docs - Manipulating the browser history
History.js polyfill
Demo page
has.js test
WebPlatform Docs
Introduction to history management