Just like puranas have different recensions, if there are different recensions of valmiki ramayana too then, are there any critical edition of ramayana to correct interpolations in it?
This website:— https://valmikiramayan.net/ is a famous translation of valmiki ramayana and a critical edition.
and it claims
This epic poem Ramayana is a smriti which is translated as "from memory". Given the antiquity of Srimad Valmiki Ramayana, there have been some interjected verses. Sometimes these verses can be contradicting. However, scholars, grammarians, historians have put lot of effort to standardize the original text, by verifying various manuscripts available from various parts of India, thus trying to stabilize and save the text from further contradictions. An example of this effort is the critical edition of Srimad Valmiki Ramayana. This site aims to study various versions of Srimad Valmiki Ramayana and arrive at a version of Ramayana that is most relevant to modern times.
The below website too mention this website
This website:— https://sanskritdocuments.org/mirrors/ramayana/valmiki.htm
"Here you can browse through the great sanskrit epic - Valimiki's Ramayana in Devanagari script. This Devanagari version of the Ramayana was converted in 1999 from Prof. John Smith 's CSX version of the original encoding of the Baroda Critical Edition of the Ramayana by Prof. Muneo Tokunaga of Kyoto, Japan.
Prof. John Smith's website has an updated version (2014) of the Critical Edition of the Valmiki Ramayana in Unicode Devanagari, Unicode Roman (using the conventions defined in ISO 15919), and ASCII (using the Harvard/Kyoto conventions) by Kanda."
Between 1020 and the introduction of printing in India in the early nineteenth century, the Rāmāyaṇa was copied by hand repeatedly in all parts of the country, and at present more than two thousand manuscripts of the poem, in whole or in part, are known to exist. The sheer size of the text, the enormous number of manuscripts, and their often discrepant testimony, make for a text-historical problem equaled in complexity, perhaps, only by that of the New Testament.
Like the Mahābhārata, the second great epic of ancient India, the Rāmāyaṇa has been handed down in two principal recensions, one from northern and one from southern India. These recensions consist of often heterogeneous versions written in the various regional scripts.
Manuscripts of the northern recension come from: Gujarat, Rajasthan, Kashmir, Nepal, Bihar, and Bengal; those of the southern recension from: Kerala, Andhra Pradesh, and Tamil Nadu, with Devanāgarī manuscripts variously affiliated to the northern and/or southern tradition.
Unlike the Mahābhārata (and this is of primary significance for the text criticism of our poem), the recensions of the Rāmāyaṇa display disagreements of a sort that cannot be accounted for by the inevitable accidents of written transmission.
In countless instances it appears that the ordering of the verses and the readings of the southern recension are far more intelligible and authentic than those of the northern recension. While its transmission, in general, seems considerably more uniform. And thus, despite some literary and historical arguments that have been made to the contrary, it recommends itself as the basis of a critical edition. But the southern recension, too, is marred by corruptions, false emendations, accretions, and the like, and does not invariably give us the right text. The northern recension can help correct it and thereby reveal the oral original.
You can access the Sanskrit (Devanāgarī) original of the CE published by the Oriental Institute (Baroda) here on archive.org. As noted in the Introduction, the Bālakāṇḍa was created out of 21 manuscripts of the Northern Recension and 16 manuscripts of the Southern Recension.
Bibek Debroy in his recent tr. based on the CE of VR talks about some interpolations that were excised from the CE:
This translation is of the Valmiki Ramayana. It is necessary to stress this point. Both the Ramayana and the Mahabharata are so popular that one is familiar with people, stories and incidents. That doesn't necessarily mean those people, stories and incidents occur in the Valmiki Ramayana in the way we are familiar with them. Just as the Bhandarkar Oriental Research Institute produced a Critical Edition of the Mahabharata, between 1951 and 1975, the Oriental Institute, Baroda, produced a Critical Edition of the Valmiki Ramayana. This translation is based on that Critical Edition, published sequentially between 1958 and 1975. Producing a Critical Edition meant sifting through a large number of manuscripts of the Valmiki Ramayana. The editors had around 2000 manuscripts to work with. Not all of these were equally reliable. Therefore, in practice, they worked with fifty to hundred manuscripts, the specific number depending on the kanda in question. It is not that there were significant differences across the manuscripts and broadly, there was a Southern Recension (version) and a Northern one, the latter sub-divided into a North Western and a North-Eastern one. The earliest of these written manuscripts dates to the eleventh century CE. In passing, the language may have been Sanskrit, but the script wasn't always Devanagari. There were scripts like Sharada, Mewari, Maithili, Bengali, Telugu, Kannada, Nandinagari, Grantha and Malayalam.
Since this translation is based on the Baroda Critical Edition, it is necessary to make another obvious point. Even within the Sanskrit Valmiki Ramayana, not everything we are familiar with is included in the Critical text. For instance, the configuration of nakshatras and planets at the time of Rama's birth is not part of the Critical text. Nor is the bulk of one of the most beautiful sections of the Valmiki Ramayana, Mandodari's lamentation. Those are shlokas that have been excised. That's also the case with a shloka that's often quoted as an illustration of Lakshmana's conduct:
नाहं जानामि केयूरं नाहं जानामि कुण्डलं ।
नुपरं तु अभिजानामि नित्यं पादाभिवन्दनात ||
This is a statement by Lakshmana to the effect that he cannot recognize the ornament on Sita's head or her earrings. Since he has always served at her feet, he can only recognize her anklets. This too has been excised. There are instances where such excision has led to a break in continuity and inconsistency and we have pointed them out in the footnotes.