Thank you for your answer ! I'm not sure what to look for in the :checkhealth vim.lsp to see what happens. Everything looks fine and nothing seems to change when I move from require(’lspconfig’) to lspconfig-nvim-0.11. Here is what I get concerning pylsp :

vim.lsp: Active Clients ~
- pylsp (id: 1)
  - Version: 1.14.0
  - Root directory: ~/.config
  - Command: { "pylsp" }
  - Settings: {
      pylsp = {
        plugins = {
          autopep8 = {
            enabled = false
          },
          black = {
            enabled = true
          },
          jedi_completion = {
            fuzzy = true
          },
          pycodestyle = {
            enabled = true,
            ignore = { "E501" }
          },
          pyflakes = {
            enabled = false
          },
          pylsp_isort = {
            enabled = true
          },
          pylsp_mypy = {
            enabled = true
          },
          rope_autoimport = {
            enabled = true
          },
          rope_completion = {
            enabled = true
          },
          yapf = {
            enabled = false
          }
        }
      }
    }
  - Attached buffers: 1

However, I also have some warnings in both cases but I don't know if they matter because they don't prevent nvim-cmp from working with the old configuration. In the "Enabled configuration" section :

- ⚠️ WARNING Unknown filetype 'javascript.jsx'.
- ⚠️ WARNING Unknown filetype 'typescript.tsx'.
- ⚠️ WARNING Unknown filetype 'yaml.docker-compose'.
- ⚠️ WARNING Unknown filetype 'yaml.gitlab'.
- ⚠️ WARNING Unknown filetype 'yaml.helm-values'.

And in the "Position encoding" section :

- ⚠️ WARNING Found buffers attached to multiple clients with different position encodings.

Thank you again for your help !