The hadith has been recorded by Tabarani and has been weakened because of the weakness of the transmitter سوار بن مصعب. See e.g. Silsilah al-Da’eefah 1781.
The meaning however is correct. Generally Islam teaches that women should stay at their homes and should avoid going out except when there is a need, or for meeting relatives, or when it is necessary to fulfill religious obligations etc.
This is corroborated in the Quran:
وقرن في بيوتكن
And abide in your houses
— Quran 33:33
معنى هذه الآية الأمر بلزوم البيت ، وإن كان الخطاب لنساء النبي صلى الله عليه وسلم فقد دخل غيرهن فيه بالمعنى . هذا لو لم يرد دليل يخص جميع النساء ، كيف والشريعة طافحة بلزوم النساء بيوتهن ، والانكفاف عن الخروج منها إلا لضرورة
The meaning of this verse is that women are commanded to remain in their homes, and while the wives of the Prophet ﷺ are addressed, other women are also included in its meaning. This would be the case even if there was no explicit specific evidence extending this to other women. Whereas in reality Shariah is filled with instructions telling women to abide in their homes and forbidding them from leaving except when there is a need.
— Tafsir al-Qurtubi
وفيه الدلالة على أن النساء مأمورات بلزوم البيوت منهيات عن الخروج
This verse is evidence that women are commanded to stay in their homes and forbidden from going out of them.
— Tafsir al-Jassas
There is also corroboration for this teaching in several other ahadith, for example there are ahadith which say that it is preferable for women to stay and pray in their homes rather than to go to mosques (Abu Dawud 570 , Abu Dawud 567). When this applies to prayer it obviously also applies to lesser reasons.
Similarly there are ahadith which say that women are permitted to go to the mosques (Muslim 442) and when there is a need (Bukhari 5237). The fact that going out in these cases is a permission implies that they are an exception and the general rule is that women were expected to abstain from leaving their homes.
It is also implied from the hadith:
المرأة عورة، وإنها إذا خرجت استشرفها الشيطان، وإنها لا تكون إلى وجه الله أقرب منها في قعر بيتها
Woman is ‘awrah (that which must be concealed), and when she goes out the Shaytaan’s hopes are raised. She is never closer to Allaah than in the inner part of her house.
— Sahih Ibn Khuzaimah and Saheeh Ibn Hibban - classed as Sahih