I will try to implement it myself :)

In the function where all the effects are updated and translated in flushTransSeq(), the function SEQ_offset_animdata(t->scene, seq, offset) can be added to translate the animdata for the effects. This is working so far. Does this implementation work @Richard Antalik (ISS) ?
Something like this:

if (ELEM(t->mode, TFM_SEQ_SLIDE, TFM_TIME_TRANSLATE)) {
  for (seq = seqbasep->first; seq; seq = seq->next) {
    if (seq->seq1 || seq->seq2 || seq->seq3) {
      SEQ_time_update_sequence(t->scene, seqbasep, seq);
      SEQ_offset_animdata(t->scene, seq, offset);
    }
  }
}

In D14187#381280, @Shrey Aggarwal (shrey_agg) wrote:

In the function where all the effects are updated and translated in flushTransSeq(), the function SEQ_offset_animdata(t->scene, seq, offset) can be added to translate the animdata for the effects. This is working so far. Does this implementation work @Richard Antalik (ISS) ?
Something like this:

if (ELEM(t->mode, TFM_SEQ_SLIDE, TFM_TIME_TRANSLATE)) {
  for (seq = seqbasep->first; seq; seq = seq->next) {
    if (seq->seq1 || seq->seq2 || seq->seq3) {
      SEQ_time_update_sequence(t->scene, seqbasep, seq);
      SEQ_offset_animdata(t->scene, seq, offset);
    }
  }
}

This would probably work, but function would have to be recursive and if you don't check for full relationship tree, then you can check only seq->seq1 and only single input effects, because for transition this would offset animdata twice as I said above.

I have noticed some code style/formatting issues, not sure if I mentioned style guide: https://wiki.blender.org/wiki/Style_Guide/C_Cpp. formatting is done automatically baced on clang-format rules, so depending on what IDE you are using, setup may be different(should be lined in wiki), or you can run make format.

Actually I have been able to make my example in last inline fail. It is relatively extreme case though:

I will try to find some bulletproof way to get needed strips and will post update if I succeed.

Sooo I think I have found the solution

I have created function that goes over relationships as you have suggested but I do actually select the strips

/* Basically, select if seq->seq1 is in collection and selected, but if there is seq->seq2, select
 * only if both seq1 and seq2 are in collection and selected. */
void transform_convert_sequencer_select_related_strips(SeqCollection *animation_strips)
{
  bool strip_selected = true;

  while (strip_selected) {
    strip_selected = false;

    Sequence *seq;
    SEQ_ITERATOR_FOREACH (seq, animation_strips) {
      if ((seq->flag & SELECT) != 0) {
        continue; /* Strip is already selected, skip it. */
      }

      if (seq->seq1 && (seq->seq1->flag & SELECT)) {
        if (seq->seq2 && (seq->seq2->flag & SELECT) == 0) {
          continue;
        }
        strip_selected = true;
        seq->flag |= SELECT;
      }
    }
  }
}

Then I do this magic:

/* Update the animation of effects*/
ListBase *seqbase = SEQ_active_seqbase_get(SEQ_editing_get(t->scene));
SeqCollection *animation_strips = SEQ_query_selected_strips(seqbase);
/* Get effect chain so we can traverse full relationship tree. */
SEQ_collection_expand(seqbase_active_get(t), animation_strips, SEQ_query_strip_effect_chain);
/* Select strips with complete relationship (all children selected). */
transform_convert_sequencer_select_related_strips(animation_strips);
/* Filter out strips with incomplete relationships, where we don't want to change animation. */
SEQ_filter_selected_strips(animation_strips);

It could fill new collection instead of selecting strip, but for transform operator this is actually good. Now issue is, that this operator already tries to do this, but id fails very badly. So sometimes you can see badly synchronized strips when moving them (should happen with my example file). So if you replace that with this complete relationship parsing, that's pretty much job done.
You can then do

if (!SEQ_transform_sequence_can_be_translated(seq))
  SEQ_offset_animdata(t->scene, seq, offset);

With what seq_transform_collection_from_transdata will output. So this will not only fix animation, but also bunch of other problems.

How did you come up with the solution? I mean parsing all the selected strips then adding their effects and removing the unwanted strips ? How did you come up with this magic :)