In order to answer the question let's first identify the key components inside a Bitcoin wallet:
Bitcoin public keys are derived by applying Elliptic Curve maths to a large random number (the private key).
A Bitcoin address is, in turn, derived by applying a series of transformations to a public key.
One private key is associated with one public key, and each public key creates one Bitcoin address. The Bitcoin wiki provides details and examples.
A standard wallet typically contains and manages several private keys and their associated public keys and addresses.
BIP32 specifies a schema for creating a Hierarchical Deterministic (HD) wallet that uses a seed phrase to reliably and repeatably generate a single master private key and set of addresses.
When we speak of "cold storage", it can mean that we either store bitcoin in
- a single standard address with a single private key, or
- an HD wallet - a set of addresses with a common master private key - all of which can be recreated from the seed phrase, or the
xprv format private key
The client mechanism for creating a standard address is different from the mechanism for creating an HD extended private key and its associated set of addresses. However, the mechanism for creating each is standardized. Wallet clients, like Electrum, can generally create addresses by either mechanism but implement their own schema for generating the HD seed phrase. Variations and changes are evident between different clients and even between different versions of the same client, e.g. the length of Electrum's seed phrase was changed some years ago.
The Bitcoin protocol accepts addresses produced by either method - the network simply sees valid Bitcoin address referenced in a transaction.
So, coming to your concern about HD client maintenance and its implications for cold storage, yes, there are risks. Who knows what the future holds, right?
Storing bitcoin, long-term, in a standard address means that you only have to back-up and secure the underlying private key. The bitcoin can be accessed easily and reliably, in future, by simply importing the private key into any standard wallet client or address tool script.
Using an HD wallet application for long-term storage could have the outcome that, after years or decades, the application has fallen out of maintenance or has changed its HD implementation. A solution would be to keep a backup of the application version that you had originally used to create the HD wallet. Also, exporting and securing the HD master private key in
xprv format could be a mitigation. However, I have witnessed instances where
xprv exports from one client fail to import to other HD clients, for whatever reason.
HD is useful and convenient for everyday use - provided it is frequently updated to new client versions. Otherwise, the HD client software will become outdated and may cease to function. Even when storing the original version, after years and decades, its dependencies on outdated software libraries and CPU/hardware architecture may render it inoperable.
For long-term cold storage a good rule of thumb is: simple and standard is safest.