Switch.

TL;DR

To switch from Claude to ChatGPT, export your data from Claude settings, open the JSON file in Chrome, and copy paste specific links to download zip files.
Use a detailed prompt to instruct ChatGPT to combine your uploaded conversation history and accessible memories into a single Markdown file.
Import the generated Markdown file into ChatGPT via the 'Add from Library' feature.
To switch from ChatGPT to Claude, copy instructions into ChatGPT, export your stored memories and context, then paste them into Claude's 'Add to memory' feature.
Skills from Claude's Codex/Skills can be downloaded as zip files and uploaded to Claude's 'Customize' section.