It seems that what you are looking for is an **HDMI audio embedder**.

It seems that the Tascam DR-701D offers this functionality as described in [Outputting this unit's audio as the HDMI output audio][1]

Examples of external alternative such products can be found here (I am not affiliated with these manufacturers, other products might exist):

[Kramer FC-69][2]

[Extron HAI 100 4K][3]

  [1]: https://tascam.jp/downloads/tascam/896/e_dr-701d_rm_vb.pdf
  [2]: https://www.kramerav.com/us/product/FC-69
  [3]: https://www.extron.com/product/hai1004k