Macbook Air Can Not Start After Trying to Remove Ubuntu

Use the following steps.

1. Boot to the same Recovery Mode used in your question.

2. Enter the following commands. None of these commands alter your Mac. The commands just product diagnostic information, which may be helpful.

   sw_vers
   export LC_CTYPE="ASCII"
   diskutil unmountdisk disk0
   dd if=/dev/disk0 count=1 bs=16 skip=13108482 | vis -cw;echo
   

   Post the output from the above commands to your question.

3. Enter the commands given below.

   diskutil unmountdisk disk0
   gpt -f add -i 2 -b 409640 -t apfs disk0
   diskutil list internal
   

   If the above commands execute successfully, then the name of the APFS volume containing macOS will appear in the output from the command diskutil list internal. If not, then post the output from the above commands to your question, post a comment to my answer and wait for my response. Otherwise, proceed.

4. Enter the following commands. When entering the commands, use the output from the previously entered diskutil list internal command to replace diskXsV with the identifier for the APFS Volume containing macOS and replace diskYsC with the identifier for the Apple_APFS Container listed as the Physical Store for the APFS Volume.

   diskutil info diskXsV | grep "Disk Size"
   diskutil info diskYsC | grep "Disk Size"
   

   If the output from both commands match, then you are done. Otherwise, proceed.

5. Enter the following commands. When entering the commands, use the output from the previously entered diskutil info diskXsV | grep "Disk Size" command to replace SizeInBlocks with the disk size in 512-Byte-Units for the APFS Volume containing macOS.

   diskutil unmountdisk disk0
   gpt -f remove -i 2 disk0
   diskutil unmountdisk disk0
   gpt -f add -i 2 -b 409640 -s SizeInBlocks -t apfs disk0
   

Use of the gpt add Command

This section can be ignored by the OP (user Gizem Kaya) . This section was added to this answer mainly to address concerns posted by user Jean_JD. The add command for gpt includes the -i, -b, -s and -t command-specific options. The table below explains how the default values are determined when one or more of these options is omitted.

If the case of this answer, the command-specific option -s was omitted from gpt -f add -i 2 -b 409640 -t apfs disk0 command in step 3. When the OP enters the command, the default value of 384370648 will be used for the size in sectors.