Praise be to Allah.
Islamic teaching is very strict concerning the ruling on what one may find of lost property in Makkah, to the extent that the Prophet (blessings and peace of Allah be upon him) said: “Its lost property is not permissible except for one who will announce it.”
Narrated by al-Bukhaari (109) and Muslim (2414).
What is meant by lost property is anything that a person may drop or lose.
What is meant by one who will announce it is one who will look for and ask about its owner.
What this hadith means is that whoever finds any property in Makkah, it is not permissible for him to pick it up unless he will stay and ask about its owner for the rest of his life, and if he dies before finding its owner, he will leave instructions to his children to ask about its owner or his heirs after him… And so on.
As for property that a person may find outside Makkah, he should ask about its owner for an entire year, then after one year has passed he may make use of it, if he does not find its owner.
This strict teaching in Islam concerning lost property in Makkah is intended to protect the property of the pilgrims performing Hajj and ‘umrah.
If a person sees lost property and knows that if he picks it up he has to look for and ask about its owner for the rest of his life, in most cases he will never pick it up; rather he will leave it where it is, and this is what will be done by everyone who sees it, until the owner of that property comes along and finds his property in the place where he lost it.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: This is one of the unique characteristics of Makkah. The difference between it and all other cities in that regard is that people leave it and go to different regions, so the one who has lost something will never be able to look for it and ask about it, in contrast to other cities.
End quote from Zaad al-Ma‘aad (3/398)
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
Lost property in Makkah al-Mukarramah (which is anything that a person may come across) is unique in that it is not permissible for anyone to pick it up except someone who wants to announce it forever, or hand it in to the authorities who deal with such property, because the Prophet (blessings and peace of Allah be upon him) said: “Its lost property is not permissible except to one who will announce it.” The wisdom behind that is that if lost property is left where it is, perhaps the owners will come back and find it. End quote from Fataawa Islamiyyah (2/311)
Based on that, anyone who finds lost property in Makkah should leave it where it is, unless there is the fear that someone may come and take it for himself, in which case he may take it and give it to those who are in charge of looking after lost property. People know that anyone who has lost something may go and ask the government department that is in charge of that.
This is the ruling on picking up lost property in Makkah.
This is what you should have done when you found that watch then picked it up.
The fact that you threw it in the trash indicates that you were afraid that you had done something haraam, so you wanted to get rid of it so that you would not fall into sin, but this was another mistake, and will not save you from the sin of having taken it, because this is wasting and destroying property, and Islam forbids us to waste wealth.
With regard to your saying that this watch had no value at all,
it is not one of the conditions of it being obligatory to look for and ask about the owner of what one finds of lost property that it should be valuable; rather the condition is that it should have value in the sense that the owner cares about it and if he loses it he will ask about it, which is usually the case with watches; their owners usually care about them and ask about them.
As you did not do what you were required to do when you picked up that watch, what you must do now is give the value of that watch in charity on behalf of its owner, and he will have the reward of that charity, and you will have repented from that mistake and absolved yourself of sin. Thus you may expiate for this sin.
It makes no difference whether you were in a state of ihram or not at the time when you picked it up.
We ask Allah, may He be exalted, to accept your repentance.
And Allah knows best.