recording real time with midi keyboard

You wrote:
I think Musescore does not have the actual "real time recording" mode...

True...
... but I think the term "real time notating" mode more accurately describes what people actually want. That is, they wish to "play", for example, a MIDI piano and have the musical score appear - similar to the "closed captioning" speech recognition software commonly used in TV broadcasting.

and:
The software should automatically pickup your note inputs and time duration.

That's the easy part. Note input and time duration is what MIDI already detects as "note on", "note off" events. (MuseScore does generate and can export MIDI.) But this information does not provide the whole story. Consider a tempo of 60 bpm in which a quarter note (theoretically) lasts one second. Then how would a staccato marking added to that quarter note be represented in MIDI? It would simply be the same note, but with a different "note off" time. How is that different from an eighth note if identical durations are "recorded" for both? What about a fermata over a half note? Not to mention accelerando/diminuendo, swing, tuplets...

So...
Music notation is more complex than simply showing "note inputs and time duration".
Notation must account for elements like time signatures and key signatures -- even as they may change within the same score. Regarding time signatures and measures, a note whose duration crosses a barline must be notated with a tie. MIDI has no concept (or need) for barlines and ties, but simply when "note off" occurs.
Also, correct note spelling (e.g., A♭ vs. G♯) often depends on the current key signature, proper chord voicing, etc.
[If you play the black key next to middle C on a piano, the space or line of the musical staff that the note gets placed on depends on whether your intention is C♯ or D♭. To MIDI it's the same piano key, same exact note either way, because MIDI doesn't use (or need) a musical staff.]

You wrote:
I think Sibelius has this recording mode.

Converting an existing MIDI "real time recording" into musical notation is difficult enough, and very often in need of final editing after the conversion into sheet music.
The more complex procedure of "real time notating" (i.e., while one "plays" a MIDI keyboard) to generate a score is the next challenge. I am not familiar with Sibelius and, like you, don't know whether it can do this -- or, if it can, how accurate the results are.